Chapter 6 Resource Masters - Morgan Park High …©Glencoe/McGraw-Hill iv Glencoe Algebra 1...

Chapter 6Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

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ISBN: 0-07-827730-2 Glencoe Algebra 1Chapter 6 Resource Masters

3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04

Glencoe/McGraw-Hill

CONSUMABLE WORKBOOKS Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.

Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7Reading to Learn Mathematics Workbook 0-07-861060-5

ANSWERS FOR WORKBOOKS The answers for Chapter 6 of these workbookscan be found in the back of this Chapter Resource Masters booklet.

StudentWorks™ This CD-ROM includes the entire Student Edition text alongwith the English workbooks listed above.

TeacherWorks™ All of the materials found in this booklet are included for view-ing and printing in the Glencoe Algebra 1 TeacherWorks CD-ROM.

© Glencoe/McGraw-Hill iii Glencoe Algebra 1

Contents

Vocabulary Builder . . . . . . . . . . . . . . . . vii

Lesson 6-1Study Guide and Intervention . . . . . . . . 343–344Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 345Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 346Reading to Learn Mathematics . . . . . . . . . . 347Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 348






Chapter 6 AssessmentChapter 6 Test, Form 1 . . . . . . . . . . . . 379–380Chapter 6 Test, Form 2A . . . . . . . . . . . 381–382Chapter 6 Test, Form 2B . . . . . . . . . . . 383–384Chapter 6 Test, Form 2C . . . . . . . . . . . 385–386Chapter 6 Test, Form 2D . . . . . . . . . . . 387–388Chapter 6 Test, Form 3 . . . . . . . . . . . . 389–390Chapter 6 Open-Ended Assessment . . . . . . 391Chapter 6 Vocabulary Test/Review . . . . . . . 392Chapter 6 Quizzes 1 & 2 . . . . . . . . . . . . . . . 393Chapter 6 Quizzes 3 & 4 . . . . . . . . . . . . . . . 394Chapter 6 Mid-Chapter Test . . . . . . . . . . . . 395Chapter 6 Cumulative Review . . . . . . . . . . . 396Chapter 6 Standardized Test Practice . . 397–398First Semester Test (Ch. 1–6) . . . . . . . . 399–402

Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1

ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A31

© Glencoe/McGraw-Hill iv Glencoe Algebra 1

Teacher’s Guide to Using theChapter 6 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 6 Resource Masters includes the core materials neededfor Chapter 6. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.

Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

WHEN TO USE Give these pages tostudents before beginning Lesson 6-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.

Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.

WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.

WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.

Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.

WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.

WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.

© Glencoe/McGraw-Hill v Glencoe Algebra 1

Assessment OptionsThe assessment masters in the Chapter 6Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions

and is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-response Bonus question.

• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.

• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questionsthat appear in the Student Edition onpages 364–365. This improves students’familiarity with the answer formats theymay encounter in test taking.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided forthe assessment masters in this booklet.

Reading to Learn MathematicsVocabulary Builder

NAME ______________________________________________ DATE ____________ PERIOD _____

66

© Glencoe/McGraw-Hill vii Glencoe Algebra 1

Voca

bula

ry B

uild

erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 6.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.

Vocabulary Term Found on Page Definition/Description/Example

Addition Property of Inequalities

boundary

compound inequality

Division Property of Inequalities

half-plane

intersection

Multiplication Property of Inequalities

(continued on the next page)

© Glencoe/McGraw-Hill viii Glencoe Algebra 1

Vocabulary Term Found on Page Definition/Description/Example

set-builder notation

Subtraction Property of Inequalities

union

Reading to Learn MathematicsVocabulary Builder (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

66

Study Guide and InterventionSolving Inequalities by Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1

© Glencoe/McGraw-Hill 343 Glencoe Algebra 1

Less

on

6-1

Solve Inequalities by Addition Addition can be used to solve inequalities. If anynumber is added to each side of a true inequality, the resulting inequality is also true.

Addition Property of InequalitiesFor all numbers a, b, and c, if a � b, then a � c � b � c, and if a � b, then a � c � b � c.

The property is also true when � and � are replaced with � and �.

Solve x � 8 � �6.Then graph it on a number line.

x � 8 � �6 Original inequality

x � 8 � 8 � �6 � 8 Add 8 to each side.

x � 2 Simplify.

The solution in set-builder notation is {x|x � 2}.Number line graph:

�4 �3 �2 �1 0 1 2 3 4

Solve 4 � 2a � �a. Thengraph it on a number line.

4 � 2a � �a Original inequality

4 � 2a � 2a � �a � 2a Add 2a to each side.

4 � a Simplify.

a � 4 4 � a is the same as a � 4.

The solution in set-builder notation is {a|a � 4}.Number line graph:

�2 �1 0 1 2 3 4 5 6

Example 1Example 1 Example 2Example 2

ExercisesExercises

Solve each inequality. Then check your solution, and graph it on a number line.

1. t � 12 � 16 2. n � 12 � 6 3. 6 � g � 3

4. n � 8 � �13 5. �12 � �12 � y 6. �6 � s � 8

Solve each inequality. Then check your solution.

7. �3x � 8 � 4x 8. 0.6n � 12 � 0.4n 9. �8k � 12 � � 9k

10. �y � 10 � 15 � 2y 11. z � � 12. �2b � �4 � 3b

Define a variable, write an inequality, and solve each problem. Then check yoursolution.

13. A number decreased by 4 is less than 14.

14. The difference of two numbers is more than 12, and one of the numbers is 3.

15. Forty is no greater than the difference of a number and 2.

4�3

1�3

�4 �2 �1 0 1 2 3�3 4�3�4 �2 �1 0 1 2 3 4�9�10 �8 �7 �6 �5 �4 �3 �2

7 8 9 10 11 12 13 14 1514 1512 13 16 17 18 19 2026 27 28 29 30 31 32 33 34


Solve Inequalities by Subtraction Subtraction can be used to solve inequalities. If anynumber is subtracted from each side of a true inequality, the resulting inequality is also true.

Subtraction Property of InequalitiesFor all numbers a, b, and c, if a � b, then a � c � b � c, and if a � b, then a � c � b � c.


Solve 3a � 5 � 4 � 2a. Then graph it on a number line.

3a � 5 � 4 � 2a Original inequality

3a � 5 � 2a � 4 � 2a � 2a Subtract 2a from each side.

a � 5 � 4 Simplify.

a � 5 � 5 � 4 � 5 Subtract 5 from each side.

a � �1 Simplify.

The solution is {aa � �1}.Number line graph:


1. t � 12 � 8 2. n � 12 � �12 3. 16 � h � 9

4. y � 4 � � 2 5. 3r � 6 � 4r 6. q � 5 � q


7. 4p � 3p � 0.7 8. r � � 9. 9k � 12 � 8k

10. � 1.2 � 2.4 � y 11. 4y � 5y� 14 12. 3n � 17 � 4n


13. The sum of a number and 8 is less than 12.

14. The sum of two numbers is at most 6, and one of the number is �2.

15. The sum of a number and 6 is greater than or equal to �4.

3�8

1�4

210 3 4 5 6 7 82 3 4 5 6 7 91 8�8 �7 �6 �5 �4 �3 �2 �1 0

1�2

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5 6 7 8 9 10 11 12 13�26 �25 �24 �23 �22 �21�6 �5 �4 �3 �2 �1 0 1 2

�4 �3 �2 �1 0 1 2 3 4

Study Guide and Intervention (continued)

Solving Inequalities by Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1

ExampleExample

ExercisesExercises

Skills PracticeSolving Inequalities by Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1


Less

on

6-1

Match each inequality with its corresponding graph.

1. x � 11 � 16 a.

2. x � 6 � 1 b.

3. x � 2 � �3 c.

4. x � 3 � 1 d.

5. x � 1 � �7 e.


6. d � 5 � 1 7. s � 9 � 8

8. a � 7 � �13 9. w � 1 � 4

10. 4 � k � 3 11. �9 � b � 4

12. �2 � x � 4 13. 2y � y � 2


14. A number decreased by 10 is greater than �5.

15. A number increased by 1 is less than 9.

16. Seven more than a number is less than or equal to �18.

17. Twenty less than a number is at least 15.

18. A number plus 2 is at most 1.

�2 �1�4 �3 0 1 2 3 4�6 �5�8 �7 �4 �3 �2 �1 0

�8 �7 �6 �5 �4 �3 �2 �1 0�2 �1�4 �3 0 1 2 3 4

2 30 1 4 5 6 7 8�8 �7 �6 �5 �4 �3 �2 �1 0

�2 �1�4 �3 0 1 2 3 42 30 1 4 5 6 7 8

0 1 2 3 4 5 6 7 8

�8 �7 �6 �5 �4 �3 �2 �1 0

876543210

43210�1�2�3�4

�8 �7 �6 �5 �4 �3 �2 �1 0


Match each inequality with its corresponding graph.

1. �8 � x � 15 a.

2. 4x � 3 � 5x b.

3. 8x � 7x � 4 c.

4. 12 � x � 9 d.


5. r � (�5) � �2 6. 3x � 8 � 4x

7. n � 2.5 � �5 8. 1.5 � y � 1

9. z � 3 � 10. � c �


11. The sum of a number and 17 is no less than 26.

12. Twice a number minus 4 is less than three times the number.

13. Twelve is at most a number decreased by 7.

14. Eight plus four times a number is greater than five times the number.

15. ATMOSPHERIC SCIENCE The troposphere extends from the earth’s surface to a heightof 6–12 miles, depending on the location and the season. If a plane is flying at analtitude of 5.8 miles, and the troposphere is 8.6 miles deep in that area, how muchhigher can the plane go without leaving the troposphere?

16. EARTH SCIENCE Mature soil is composed of three layers, the uppermost being topsoil.Jamal is planting a bush that needs a hole 18 centimeters deep for the roots. Theinstructions suggest an additional 8 centimeters depth for a cushion. If Jamal wants toadd even more cushion, and the topsoil in his yard is 30 centimeters deep, how muchmore cushion can he add and still remain in the topsoil layer?

�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4

3�4

1�2

2�3

�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4

4 52 3 6 7 8 9 10�8 �7 �6 �5 �4 �3 �2 �1 0

2 3 4 5 6 7 810

�8 �7 �6 �5 �4 �3 �2 �1 0

876543210

210�1�2�3�4�5�6

Practice Solving Inequalities by Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1

Reading to Learn MathematicsSolving Inequalities by Addition and Subtraction

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1


Less

on

6-1

Pre-Activity How are inequalities used to describe school sports?

Read the introduction to Lesson 6-1 at the top of page 318 in your textbook.

• Use the information in the graph to write an inequality statement aboutparticipation in two sports.

• Rewrite your inequality statement to show that 40 schools added both ofthe sports. Is the statement still true?

Reading the LessonWrite the letter of the graph that matches each inequality.

1. x � �1 a.

2. x � �1 b.

3. x � �1 c.

4. x � �1 d.

5. Use the chart to write a sentence that could be described by the inequality 3n � 2n � 7.Then solve the inequality.

Inequalities

� � � �

less than greater than at most at leastfewer than more than no more than no less than

less than or equal to greater than or equal to

Helping You Remember

6. Teaching someone else can help you remember something. Explain how you would teachanother student who missed class to solve the inequality 2x � 4 � 3x.

3210�1�2�3

3210�1�2�3

�3 �2 �1 0 1 2 3

�3 �2 �1 0 1 2 3


Triangle InequalitiesRecall that a line segment can be named by the letters of its endpoints. Line segment AB (written as A�B�) has points A and B forendpoints. The length of AB is written without the bar as AB.

AB � BC m�A � m�B

The statement on the left above shows that A�B� is shorter than B�C�.The statement on the right above shows that the measure of angle Ais less than that of angle B.

These three inequalities are true for any triangle ABC,no matter how long the sides.

a. AB � BC � ACb. If AB � AC, then m�C � m�B.c. If m�C � m�B, then AB � AC.

Use the three triangle inequalities for these problems.

1. List the sides of triangle DEF in order of increasing length.

2. In the figure at the right, which line segment is the shortest?

3. Explain why the lengths 5 cm, 10 cm, and 20 cm could not be usedto make a triangle.

4. Two sides of a triangle measure 3 in. and 7 in. Between which twovalues must the third side be?

5. In triangle XYZ, XY 15, YZ 12, and XZ 9. Which is thegreatest angle? Which is the least?

6. List the angles �A, �C, �ABC, and �ABD, in order of increasing size. C

A

DB

13

15

12

5

9

JM

K

L

65�

60�65�55�

65�50�

D

F E60� 35�

85�

A

B C

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1

Study Guide and InterventionSolving Inequalities by Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2


Less

on

6-2

Solve Inequalities by Multiplication If each side of an inequality is multiplied bythe same positive number, the resulting inequality is also true. However, if each side of aninequality is multiplied by the same negative number, the direction of the inequality mustbe reversed for the resulting inequality to be true.

For all numbers a, b, and c, with c 0,

1. if c is positive and a � b, then ac � bc;Multiplication Property of Inequalities if c is positive and a � b, then ac � bc;

2. if c is negative and a � b, then ac � bc;if c is negative and a � b, then ac � bc.


Solve � � 12.

� � 12 Original equation

(�8)�� (�8)12 Multiply each side by �8; change � to �.

y � �96 Simplify.

The solution is {yy � �96}.

y�8

y�8

y8

Solve k � 15.

k � 15 Original equation

� � k � � �15 Multiply each side by .

k � 20 Simplify.

The solution is {kk � 20}.

4�3

4�3

3�4

4�3

3�4

34


ExercisesExercises


1. � 2 2. � � 22 3. h � �3 4. � � �6

5. n � 10 6. � b � 7. � � 8. �2.51 � �

9. � �2 10. � � � 11. � 5.4 12. � �6


13. Half of a number is at least 14.

14. The opposite of one-third a number is greater than 9.

15. One fifth of a number is at most 30.

2a�7

n�10

9p�5

3�4

g�5

2h�4

3�20

3m�5

1�3

2�3

1�4

p�6

3�5

n�50

y�6


Solve Inequalities by Division If each side of a true inequality is divided by thesame positive number, the resulting inequality is also true. However, if each side of aninequality is divided by the same negative number, the direction of the inequality symbolmust be reversed for the resulting inequality to be true.

For all numbers a, b, and c with c 0,

Division Property 1. if c is positive and a � b, then � ; if c is positive and a � b, then � ;of Inequalities

2. if c is negative and a � b, then � ; if c is negative and a � b, then � .


Solve �12y � 48.

�12y � 48 Original inequality

� Divide each side by �12 and change � to �.

y � �4 Simplify.

The solution is { yy � �4}.


1. 25g � �100 2. �2x � 9 3. �5c � 2 4. �8m � �64

5. �6k � 6. 18 � �3b 7. 30 � �3n 8. �0.24� 0.6w

9. 25 � �2m 10. �30 � �5p 11. �2n � 6.2 12. �35 � 0.05h

13. �40 � 10h 14. � n � 6 15. �3 �


16. Four times a number is no more than 108.

17. The opposite of three times a number is greater than 12.

18. Negative five times a number is at most 100.

p�4

2�3

1�5

48��12

�12y��12

b�c

a�c

b�c

a�c

b�c

a�c

b�c

a�c


Solving Inequalities by Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2

ExampleExample

ExercisesExercises

Skills PracticeSolving Inequalities by Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2


Less

on

6-2

Match each inequality with its corresponding statement.

1. 3n � 9 a. Three times a number is at most nine.

2. n � 9 b. One third of a number is no more than nine.

3. 3n � 9 c. Negative three times a number is more than nine.

4. �3n � 9 d. Three times a number is less than nine.

5. n � 9 e. Negative three times a number is at least nine.

6. �3n � 9 f. One third of a number is greater than or equal to nine.


7. 14g � 56 8. 11w � 77 9. 20b � �120 10. �8r � 16

11. �15p � �90 12. � 9 13. � �15 14. � � �9

15. � � 6 16. 5z � �90 17. �13m � �26 18. � �17

19. �y � 36 20. �16c � �224 21. � � 2 22. 12 �


23. Four times a number is greater than �48.

24. One eighth of a number is less than or equal to 3.

25. Negative twelve times a number is no more than 84.

26. Negative one sixth of a number is less than �9.

27. Eight times a number is at least 16.

d�12

h�10

k�5

t�12

p�7

a�9

s�4

1�3

1�3


Match each inequality with its corresponding statement.

1. �4n � 5 a. Negative four times a number is less than five.

2. n � 5 b. Four fifths of a number is no more than five.

3. 4n � 5 c. Four times a number is fewer than five.

4. n � 5 d. Negative four times a number is no less than five.

5. 4n � 5 e. Four times a number is at most five.

6. �4n � 5 f. Four fifths of a number is more than five.


7. � � �14 8. �13h � 52 9. � �6 10. 39 � 13p

11. n � �12 12. � t � 25 13. � m � �6 14. k � �10

15. �3b � 0.75 16. �0.9c � �9 17. 0.1x � �4 18. �2.3 �

19. �15y � 3 20. 2.6v � �20.8 21. 0 � �0.5u 22. f � �1


23. Negative three times a number is at least 57.

24. Two thirds of a number is no more than �10.

25. Negative three fifths of a number is less than �6.

26. FLOODING A river is rising at a rate of 3 inches per hour. If the river rises more than 2feet, it will exceed flood stage. How long can the river rise at this rate without exceedingflood stage?

27. SALES Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If thestore wants to make a profit of no less than $5225, how many bags of dog food does itneed to sell?

7�8

j�4

10�3

3�5

5�9

2�3

s�16

a�5

4�5

4�5

Practice Solving Inequalities by Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2

Reading to Learn MathematicsSolving Inequalities by Multiplication and Division

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2


Less

on

6-2

Pre-Activity Why are inequalities important in landscaping?


• Would a wall 6 bricks high be lower than a wall 6 blocks high? Why?

• Would a wall n bricks high be lower than a wall n blocks high? Explain.

Reading the Lesson

1. Write an inequality that describes each situation.

a. A number n divided by 8 is greater than 5.

b. Twelve times a number k is at least 7.

c. A number x divided by �10 is less than or equal to 50.

d. Three fifths of a number n is at most 13.

e. Nine is greater than or equal to one half of a quantity m.

2. Use words to tell what each inequality says.

a. 12 � 6n

b. � 14

c. 11x � 32


3. In your own words, write a rule for multiplying and dividing inequalities by positive andnegative numbers.

t��3


The Maya 'I'he Maya were a Native American people who lived from about1500 B.C. to about 1500 A.D. in the region that today encompassesmuch of Central America and southern Mexico. Their manyaccomplishments include exceptional architecture, pottery,painting, and sculpture, as well as significant advances in thefields of astronomy and mathematics.

The Maya developed a system of numeration that was based onthe number twenty. The basic symbols of this system are shown inthe table at the right. The places in a Mayan numeral are writtenvertically—the bottom place represents ones, the place aboverepresents twenties, the place above that represents 20 � 20, orfour hundreds, and so on. For instance, this is how to write thenumber 997 in Mayan numerals.

← 2 � 800

← 9 � 180

← 17 � 17997

Evaluate each expression when v , w , x , y , and z . Then write the answer in Mayan numerals. Exercise 5 is done for you.

1. 2. 3. xv

4. vxy 5. wx � z 6. vz � xy

7. w(v � x � z) 8. vwz 9. z(wx � x)

Tell whether each statement is true or false.

10. � � 11. 12.

13. ( � ) � � ( � )

14. How are Exercises 10 and 11 alike? How are they different?

_______________• • •_______________• • •

• • •____________________

• • •_______________

•_____

• • •__________

• • •__________

•_____• • •__________•_____•_____• • •__________

●●●●

• • •

●●●●

●●●●

v � w � z��x

z�w

• •__________●●●●• • • •• • • _______________•_____

1• •_______________

20• • • •_____

400• •

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2

0 10

1 11

2 12

3 13

4 14

5 15

6 16

7 17

8 18

9 19 • • • •_______________• • • •_____

• • • _______________• • •_____

• •_______________• •_____

•_______________•_____

____________________

• • • •__________• • • •

• • •__________• • •

• •__________• •

•__________•

__________●●●●

Study Guide and InterventionSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3


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Solve Multi-Step Inequalities To solve linear inequalities involving more than oneoperation, undo the operations in reverse of the order of operations, just as you would solvean equation with more than one operation.

Solve 6x � 4 � 2x � 12.

6x � 4 � 2x � 12 Original inequality

6x � 4 � 2x � 2x � 12 � 2x Subtract 2x from

each side.

4x � 4 � 12 Simplify.

4x � 4 � 4 � 12 � 4 Add 4 to each side.

4x � 16 Simplify.

� Divide each side by 4.

x � 4 Simplify.

The solution is {xx � 4}.

16�4

4x�4

Solve 3a � 15 � 4 � 5a.

3a � 15 � 4 � 5a Original inequality

3a � 15 � 5a � 4 � 5a � 5a Subtract 5a from

each side.

�2a � 15 � 4 Simplify.

�2a � 15 � 15 � 4 � 15 Add 15 to each side.

�2a � 19 Simplify.

�Divide each side by �2

and change � to �.

a � �9 Simplify.

The solution is �aa � �9 �.1�2

1�2

19��2

�2a��2


ExercisesExercises


1. 11y � 13 � �1 2. 8n � 10 � 6 � 2n 3. � 1 � �5

4. 6n � 12 � 8 � 8n 5. �12 � d � �12 � 4d 6. 5r � 6 � 8r � 18

7. � 12 8. 7.3y � 14.4 � 4.9y 9. �8m � 3 � 18 � m

10. �4y � 10 � 19 � 2y 11. 9n � 24n � 45 � 0 12. � �4


13. Negative three times a number plus four is no more than the number minus eight.

14. One fourth of a number decreased by three is at least two.

15. The sum of twelve and a number is no greater than the sum of twice the number and �8.

4x � 2�5

�3x � 6��2

q�7


Solve Inequalities Involving the Distributive Property When solvinginequalities that contain grouping symbols, first use the Distributive Property to remove thegrouping symbols. Then undo the operations in reverse of the order of operations, just as youwould solve an equation with more than one operation.

Solve 3a � 2(6a � 4) � 4 � (4a � 6).

3a � 2(6a � 4) � 4 � (4a � 6) Original inequality

3a � 12a � 8 � 4 � 4a � 6 Distributive Property

�9a � 8 � �2 � 4a Combine like terms.

�9a � 8 � 4a � �2 � 4a � 4a Add 4a to each side.

�5a � 8 � �2 Combine like terms.

�5a � 8 � 8 � �2 � 8 Subtract 8 from each side.

�5a � �10 Simplify.

a � 2 Divide each side by �5 and change � to �.

The solution in set-builder notation is {aa � 2}.


1. 2(t � 3) � 16 2. 3(d � 2) � 2d � 16 3. 4h � 8 � 2(h � 1)

4. 6y � 10 � 8 � (y � 14) 5. 4.6(x � 3.4) � 5.1x 6. �5x � (2x � 3) � 1

7. 3(2y � 4) � 2(y � 1) � 10 8. 8 � 2(b � 1) � 12 � 3b 9. �2(k � 1) � 8(1� k)

10. 0.3( y � 2) � 0.4(1 � y) 11. m � 17 � �(4m � 13)

12. 3n � 8 � 2(n � 4) � 2(1 � n) 13. 2(y � 2) � �4 � 2y

14. k � 17 � �(17 � k) 15. n � 4 � � 3(2 � n)


16. Twice the sum of a number and 4 is less than 12.

17. Three times the sum of a number and six is greater than four times the numberdecreased by two.

18. Twice the difference of a number and four is less than the sum of the number and five.


Solving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3

ExampleExample

ExercisesExercises

Skills PracticeSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3


Less

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6-3

Justify each indicated step.

1. t � 3 � �15

t � 3 � 3 � �15 � 3 a.

t � �12

� �t � (�12) b.

t � �16

2. 5(k � 8) � 7 � 235k � 40 � 7 � 23 a.

5k � 33 � 235k � 33 � 33 � 23 � 33 b.

5k � �10

� c.

k � �2

?�10�5

5k�5

?

?

?4�3

3�4

4�3

3�4

?3�4

3�4


3. �2b � 4 � �6 4. 3x � 15 � 21 5. � 1 � 3

6. a � 4 � 2 7. � � 7 � �4 8. j � 10 � 5

9. � f � 3 � �9 10. 2p � 5 � 3p � 10 11. 4k � 15 � �2k � 3

12. 2(�3m � 5) � �28 13. �6(w � 1) � 2(w � 5) 14. 2(q � 3) � 6 � �10


15. Four more than the quotient of a number and three is at least nine.

16. The sum of a number and fourteen is less than or equal to three times the number.

17. Negative three times a number increased by seven is less than negative eleven.

18. Five times a number decreased by eight is at most ten more than twice the number.

19. Seven more than five sixths of a number is more than negative three.

20. Four times the sum of a number and two increased by three is at least twenty-seven.

2�3

3�4

t�5

2�5

d�2


Justify each indicated step.

Practice Solving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3

1. x �

8x � (8) a.

8x � 5x � 128x � 5x � 5x � 12 � 5x b.

3x � �12

� c.

x � �4

2. 2(2h � 2) � 2(3h � 5) � 124h � 4 � 6h � 10 � 12 a.4h � 4 � 6h � 2

4h � 4 � 6h � 6h � 2 � 6h b.�2h � 4 � �2

�2h � 4 � 4 � �2 � 4 c.�2h � �6

� d.

h � 3

?�6��2

�2h��2

?

?

?

?�12�3

3x�3

?

?5x � 12�8

5x � 12�8


3. �5 � � �9 4. 4u � 6 � 6u � 20 5. 13 � a � 1

6. � �8 7. � 7

8. h � 9. 3(z � 1) � 11 � �2(z � 13)

10. 3e � 2(4e � 2) � 2(6e � 1) 11. 5n � 3(n � 6) � 0


12. A number is less than one fourth the sum of three times the number and four.

13. Two times the sum of a number and four is no more than three times the sum of thenumber and seven decreased by four.

14. GEOMETRY The area of a triangular garden can be no more than 120 square feet. Thebase of the triangle is 16 feet. What is the height of the triangle?

15. MUSIC PRACTICE Nabuko practices the violin at least 12 hours per week. Shepractices for three fourths of an hour each session. If Nabuko has already practiced 3 hours in one week, how many sessions remain to meet or exceed her weekly practice goal?

6h � 3�5

3f � 10�5

w � 3�2

2�3

t�6

Reading to Learn MathematicsSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3


Less

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6-3

Pre-Activity How are linear inequalities used in science?

Read the introduction to Lesson 6-3 at the top of page 332 in your textbook.Then write an inequality that could be used to find the temperatures indegrees Celsius for which each substance is a gas.

Argon: Bromine:

Reading the Lesson

1. What does the phrase “undoing the operations in reverse of the order of operations” mean?

2. Describe how checking the solution of an inequality is different from checking thesolution of an equation.

3. Describe how the Distributive Property can be used to remove the grouping symbols inthe inequality 4x � 7(2x � 8) � 3x � 5.

4. Is it possible to have no solution when you solve an inequality? Explain your answer andgive an example.


5. Make a checklist of steps you can use when solving inequalities.


Carlos Montezuma During his lifetime, Carlos Montezuma (1865?–1923) was one of themost influential Native Americans in the United States. He wasrecognized as a prominent physician and was also a passionate advocateof the rights of Native American peoples. The exercises that follow willhelp you learn some interesting facts about Dr. Montezuma’s life.

Solve each inequality. The word or phrase next to the equivalent inequality will complete the statement correctly.

1. �2k � 10 2. 5 � r � 9 Montezuma was born in the state He was a Native American of the of . Yavapais, who are a people.

a. k � �5 Arizona a. r � �4 Navajo

b. k � �5 Montana b. r � �4 Mohawk

c. k � 12 Utah c. r � 14 Mohave-Apache

3. �y � �9 4. �3 � q � 12 Montezuma received a medical As a physician, Montezuma's field of degree from in 1889. specialization was .

a. y � 9 Chicago Medical College a. q � �4 heart surgery

b. y � �9 Harvard Medical School b. q � 15 internal medicine

c. y � 9 Johns Hopkins University c. q � �15 respiratory diseases

5. 5 � 4x � 14 � x 6. 7 � t � 7 � tFor much of his career, he maintained In addition to maintaining his medicala medical practice in . practice, he was also a(n) .

a. x � 9 New York City a. t � 7 director of a blood bank

b. x � 3 Chicago b. t � 0 instructor at a medical college

c. x � �9 Boston c. t � �7 legal counsel to physicians

7. 3a � 8 � 4a � 10 8. 6n � 8n � 12 Montezuma founded, wrote, and Montezuma testified before a edited , a monthly newsletter committee of the United States that addressed Native American Congress concerning his work in concerns. treating .

a. a � �2 Yavapai a. n � 6 appendicitis

b. a � 18 Apache b. n � �6 asthma

c. a � 18 Wassaja c. n � �10 heart attacks

?

?

??

??

??

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3

Study Guide and InterventionSolving Compound Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4


Less

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Inequalities Containing and A compound inequality containing and is true only ifboth inequalities are true. The graph of a compound inequality containing and is theintersection of the graphs of the two inequalities. Every solution of the compoundinequality must be a solution of both inequalities.

Graph the solutionset of x � 2 and x � �1.

Graph x � 2.

Graph x � �1.

Find the intersection.

The solution set is {x�1 � x � 2}.

�2 �1�3 0 1 2 3

�3 �2 �1 0 1 2 3

�3 �2 �1 0 1 2 3

Solve �1 � x � 2 � 3 usingand. Then graph the solution set.

�1 � x � 2 and x � 2 � 3�1 � 2 � x � 2 � 2 x � 2 � 2 � 3 � 2

�3 � x x � 1

Graph x � �3.

Graph x � 1.

Find the intersection.

The solution set is {x�3 � x � 1}.

�2 �1�4 �3 0 1 2

�3�4 �2 �1 0 1 2

�3�4 �2 �1 0 1 2


ExercisesExercises

Graph the solution set of each compound inequality.

1. b � �1 and b � 3 2. 2 � q � �5 3. x � �3 and x � 4

4. �2 � p � 4 5. �3 � d and d� 2 6. �1 � p � 3

Solve each compound inequality. Then graph the solution set.

7. 4 � w � 3 � 5 8. �3 � p � 5 � 2

9. �4 � x � 2 � �2 10. y � 1� 2 and y � 2 � 1

11. n � 2 � �3 and n � 4 � 6 12. d � 3 � 6d � 12 � 2d � 32

�3 �2 �1 0 1 2 3 4 5�3�4 �2 �1 0 1 2 3 4

�3�4 �2 �1 0 1 2 3 4�7 �6 �5 �4 �3 �2 �1 0 1

0 1 2 3 4 5 6 7 8�3�4 �2 �1 0 1 2 3 4

�3�4 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4�3 �2 �1 0 1 2 3 4 5

�4 �3 �2 �1 0 1 2 3 4�4 �3�6 �5 �2 �1 0 1 2�4 �3 �2 �1 0 1 2 3 4


Inequalities Containing or A compound inequality containing or is true if one orboth of the inequalities are true. The graph of a compound inequality containing or is theunion of the graphs of the two inequalities. The union can be found by graphing bothinequalities on the same number line. A solution of the compound inequality is a solution ofeither inequality, not necessarily both.

Solve 2a � 1 � 11 or a � 3a � 2.

2a � 1 � 11 or a � 3a � 22a � 1 � 1 � 11 � 1 a � 3a � 3a � 3a � 2

2a � 10 �2a � 2

� �

a � 5 a � �1

Graph a � 5.

Graph a � �1.

Find the union.

The solution set is {aa � 5}.


1. b � 2 or b � �3 2. 3 � q or q � 1 3. y � �4 or y � 0

4. 4 � p or p � 8 5. �3 � d or d � 2 6. �2 � x or 3 � x


7. 3 � 3w or 3w � 9 8. �3p � 1 � �11 or p � 2

9. 2x � 4 � 6 or x � 2x � 4 10. 2y � 2 � 12 or y � 3 � 2y

11. n � �2 or 2n � 2 � 6 � n 12. 3a � 2 � 5 or 7 � 3a � 2a � 6

0�1�2�3�4 1 2 3 40�1�2�3�4 1 2 3 4

1�2

0 1 2 3 4 5 6 7 8�2 �1 0 1 2 3 4 5 6

0 1 2 3 4 5 6 7 8�3�4 �2 �1 0 1 2 3 4

�3�4 �2 �1 0 1 2 3 40�1�2�3�4 1 2 3 40�1�2 1 2 3 4 5 6

�3�4�5 �2 �1 0 1 2 3�3�4 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4

�2 �1 0 1 2 3 4 5 6

�2 �1 0 1 2 3 4 5 6

�2 �1 0 1 2 3 4 5 6

2��2

�2a��2

10�2

2a�2


Solving Compound Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4

ExampleExample

ExercisesExercises

Skills PracticeSolving Compound Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4


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6-4


1. b � 3 or b � 0 2. z � 3 and z � �2

3. k � 1 and k � 5 4. y � �1 or y � 1

Write a compound inequality for each graph.

5. 6.

7. 8.


9. m � 3 � 5 and m � 3 � 7 10. y � 5 � �4 or y � 5 � 1

11. 4 � f � 6 and f � 6 � 5 12. w � 3 � 0 or w � 7 � 9

13. �6 � b � 4 � 2 14. p � 2 � �2 or p � 2 � 1


15. A number plus one is greater than negative five and less than three.

16. A number decreased by two is at most four or at least nine.

17. The sum of a number and three is no more than eight or is more than twelve.

�3�4 �2 �1 0 1 2 3 4�2 �1 0 1 2 3 4 5 6

�3�4 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4

�2 �1 0 1 2 3 4 5 6�2 �1 0 1 2 3 4 5 6

�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4

�2 �1 0 1 2 3 4 5 6�2 �1�4 �3 0 1 2 3 4

�3�4 �2 �1 0 1 2 3 40 1 2 3 4 5 6 7 8

�4 �3 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4



1. �4 � e � 1 2. x � 0 or x � 3

3. g � �3 or g � 4 4. �4 � p � 4

Write a compound inequality for each graph.

5. 6.

7. 8.


9. k � 3 � �7 or k � 5 � 8 10. �n � 2 or 2n � 3 � 5

11. 5 � 3h � 2 � 11 12. 2c � 4 � �6 and 3c � 1 � 13


13. Two times a number plus one is greater than five and less than seven.

14. A number minus one is at most nine, or two times the number is at least twenty-four.

METEOROLOGY For Exercises 15 and 16, use the following information.Strong winds called the prevailing westerlies blow from west to east in a belt from 40° to60° latitude in both the Northern and Southern Hemispheres.

15. Write an inequality to represent the latitude of the prevailing westerlies.

16. Write an inequality to represent the latitudes where the prevailing westerlies are not located.

17. NUTRITION A cookie contains 9 grams of fat. If you eat no fewer than 4 and no more than7 cookies, how many grams of fat will you consume?

�2 �1 0 1 2 3 4 5 6�2 �1�4 �3 0 1 2 3 4

�4 �3 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4

�2�3�4�5�6 �1 0 1 2�2 �1 0 1 2 3 4 5 6

�2 �1 0 1 2 3 4 5 6�4 �3 �2 �1 0 1 2 3 4

�2 �1�4 �3 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4

0�1�2�3�4 1 2 3 4�2 �1�4 �3�6 �5 0 1 2

Practice Solving Compound Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4

Reading to Learn MathematicsSolving Compound Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4


Less

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6-4

Pre-Activity How are compound inequalities used in tax tables?


• Explain why it is possible that Mr. Kelly’s income is $41,370.

• Explain why it is not possible that Mr. Kelly’s income is $41,400.

Reading the Lesson

1. When is a compound inequality containing and true?

2. The graph of a compound inequality containing and is the of thegraphs of the two inequalities.

3. When is a compound inequality containing or true?

4. The graph of a compound inequality containing or is the of thegraphs of the two inequalities.

5. Suppose you use yellow to show the graph of Inequality #1 on the number line. You useblue to show the graph of Inequality #2. Write and or or in each blank to complete thesentence.

a. The part that is green is the graph of Inequality #1 Inequality #2.

b. All colored parts form the graph of Inequality #1 Inequality #2.


6. One way to remember something is to connect it to something that is familiar to you.Write two true compound statements about yourself, one using the word and and theother using the word or.


Some Properties of InequalitiesThe two expressions on either side of an inequality symbol aresometimes called the first and second members of the inequality.

If the inequality symbols of two inequalities point in the samedirection, the inequalities have the same sense. For example, a � band c � d have the same sense; a � b and c � d have opposite senses.

In the problems on this page, you will explore some properties of inequalities.

Three of the four statements below are true for all numbers aand b (or a, b, c, and d). Write each statement in algebraicform. If the statement is true for all numbers, prove it. If it isnot true, give an example to show that it is false.

1. Given an inequality, a new and equivalent inequality can becreated by interchanging the members and reversing the sense.

2. Given an inequality, a new and equivalent inequality can be createdby changing the signs of both terms and reversing the sense.

3. Given two inequalities with the same sense, the sum of thecorresponding members are members of an equivalent inequalitywith the same sense.

4. Given two inequalities with the same sense, the difference of thecorresponding members are members of an equivalent inequalitywith the same sense.

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4

Study Guide and InterventionSolving Open Sentences Involving Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5


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Absolute Value Equations When solving equations that involve absolute value, thereare two cases to consider.Case 1: The value inside the absolute value symbols is positive.Case 2: The value inside the absolute value symbols is negative.

Solve x � 4 1. Thengraph the solution set.

Write x � 4 1 as x � 4 1 or x � 4 �1.

x � 4 1 or x � 4 �1x � 4 � 4 1 � 4 x � 4 �1

x �3 x � 4 � 4 �1� 4x �5

The solution set is {�5, �3}.The graph is shown below.

�8 �7 �6 �5 �4 �3 �2 �1 0

Write an inequalityinvolving absolute value for the graph.

Find the point that is the same distancefrom �2 as it is from 4.

The distance from 1 to �2 is 3 units. Thedistance from 1 to 4 is 3 units.So, x � 1 3.

10�1�2�3 2 3

3 units 3 units

4 5

�3 �2 �1 0 1 2 3 4 5


ExercisesExercises

Solve each open sentence. Then graph the solution set.

1. y 3 2. x � 4 4 3. y � 3 2

4. b � 2 3 5. w � 2 5 6. t � 2 4

7. 2x 8 8. 5y � 2 7 9. p � 0.2 0.5

10. d � 100 50 11. 2x � 1 11 12. 3x � 6

For each graph, write an open sentence involving absolute value.

13. 14. 15.�3�4�5�6�7 �2 �1 0 1�3�4 �2 �1 0 1 2 3 40�2�4�6�8 2 4 6 8

�2�3 �1 0 1 2 3 4 5�4�6 �2 0 2 4 6 8 1050 100 150 200

1�2

�0.8 �0.4 0 0.4 0.8�3�4 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4

�8 �6 �4 �2 0 2 4 6 8�8 �6 �4 �2 0 2 4 6 8�6 �5 �4 �3 �2 �1 0 1 2

�8 �7 �6 �5 �4 �3 �2 �1 00 1 2 3 4 5 6 7 8�3�4 �2 �1 0 1 2 3 4


Absolute Value Inequalities When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving � (or �) and two cases to consider for inequalities involving � (or �).

Remember that inequalities with and are related to intersections, while inequalities with or are related to unions.

Solve |3a � 4| � 10. Then graph the solution set.

Write 3a � 4 � 10 as 3a � 4 � 10 and 3a � 4 � �10.3a � 4 � 10 and 3a � 4 � �10

3a � 4 � 4 � 10 � 4 3a � 4 � 4 � �10 � 43a � 6 3a � �14

� �

a � 2 a � �4

The solution set is �a�4 � a � 2�.


1. c � 2 � 6 2. x � 9 � 0 3. 3f � 10 � 4

4. x � 2 5. x � 3 6. 2x � 1 � �2

7. 2d � 1 � 4 8. 3 � (x � 1) � 8 9. 3r � 2 � �5


10. 11. 12.�2 �1�3 0 1 2 3 4 5�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4

�4 �3 �2 �1 0 1 2 3 4�4 �2 0 2 4 6 8 10 12�4 �3 �2 �1 0 1 2 3 4

0�1�2�3�4 1 2 3 40�1�2�3�4 1 2 3 4�4 �3 �2 �1 0 1 2 3 4

�6 �5 �4 �3 �2 �1 0 1 2�4 �3 �2 �1 0 1 2 3 420�2�4�6 4 6 8 10

2�3

2�3

�14�3

3a�3

6�3

3a�3

If x � n, then x � �n and x � n.If x � n, then x � n or x � �n.


Solving Open Sentences Involving Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5

ExampleExample

ExercisesExercises

Now graph the solution set.

�2 �1�4�5 �3 0 1 2 3

Skills PracticeSolving Open Sentences Involving Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5


Less

on

6-5

Match each open sentence with the graph of its solution set.

1. x � 2 a.

2. x � 5 3 b.

3. x � 2 � 3 c.

4. x � 1 � 4 d.

Express each statement using an inequality involving absolute value. Do not solve.

5. The weatherman predicted that the temperature would be within 3° of 52°F.

6. Serena will make the B team if she scores within 8 points of the team average of 92.

7. The dance committee expects attendance to number within 25 of last year’s 87 students.


8. s � 1 5 9. c � 3� 1

10. n � 2 � 1 11. t � 6 � 4

12. w � 2 2 13. k � 5 � 4


14. 15.

16. 17.�2�3�4�5 �1 0 1 2 3 4 5�2�3�4�5 �1 0 1 2 3 4 5

�2�3�4�5�6�7 �1 0 1 2 3�5 �4 �3 �2 �1 0 1 2 3 4 5

0 1 2 3 4 5 6 7 8 9 10�3�4 �2 �1 0 1 2 3 4 5 6

�8 �7�10 �9 �6 �5 �4 �3 �2 �1 0�2 �1�4�5�6 �3 0 1 2 3 4

�3 �1 0 1 2 3 4 5 6�2 7�3�4�5�6 �2 �1 0 1 2 3 4

�2�3�4 �1 0 1 2 3 4 5 6

�2�3�4�5 �1 0 1 2 3 4 5

�2�3�4�5 �1 0 1 2 3 4 5

�8�9�10 �7 �6 �5 �4 �3 �2 �1 0


Match each open sentence with the graph of its solution set.

1. x � 7 3 a.

2. x � 3 � 1 b.

3. 2x � 1 � 5 c.

4. 5 � x � 3 d.

Express each statement using an inequality involving absolute value. Do not solve.

5. The height of the plant must be within 2 inches of the standard 13-inch show size.

6. The majority of grades in Sean’s English class are within 4 points of 85.


7. |2z � 9| � 1 8. |3 � 2r| � 7

9. |3t � 6| � 9 10. |2g � 5| � 9


11. 12.

13. 14.

15. FITNESS Taisha uses the elliptical cross-trainer at the gym. Her general goal is to burn280 Calories per workout, but she varies by as much as 25 Calories from this amount onany given day. What is the range of the number of Calories burned for Taisha’s cross-trainer workout?

16. TEMPERATURE A thermometer is guaranteed to give a temperature no more than1.2°F from the actual temperature. If the thermometer reads 28°F, what is the range forthe actual temperature?

�2�3 �1 0 1 2 3 4 5 6 7�2�3�4�5�6�7�8 �1 0 1 2

�2�3�4�5�6�7�8 �1 0 1 21 2 3 4 5 6 7 8 9 10 11

�2 �1 0 1 2 3 4 5 6 7 8�5 �4 �3 �2 �1 0 1 2 3 4 5

�5 �4 �3 �2 �1 0 1 2 3 4 5�5 �4 �3 �2 �1 0 1 2 3 4 5

�2�3�4�5 �1 0 1 2 3 4 5

�8�9�10 �7 �6 �5 �4 �3 �2 �1 0

�2 �1 0 1 2 3 4 5 6 7 8

�2�3�4�5 �1 0 1 2 3 4 5

Practice Solving Open Sentences Involving Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5

Reading to Learn MathematicsSolving Open Sentences Involving Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5


Less

on

6-5

Pre-Activity How is absolute value used in election polls?


• What does the phrase margin of error mean to you?

• In this poll, the number of people opposed to the tax levy may be as

high as or as low as . This can be written as

the inequality x � � 3.

Reading the Lesson

Complete each compound sentence by writing and or or in the blank. Use theresult to help you graph the absolute value sentence.

Absolute ValueSentence

Compound Sentence Graph

1. 2x � 2 8 2x � 2 8 2x � 2 �8

2. x � 5 � 4 x � 5 � 4 x � 5 � �4

3. 2x � 3 � 5 2x � 3 � 5 2x � 3 � �5

4. How would you write the compound sentence 3x � 7 � 5 or 3x � 7 � �5 as an absolutevalue sentence?


5. Recall that x tells you how many units the number x is from zero on the number line.Explain the meaning of x n, x � n, and x � n by using the idea of the distancefrom x to zero.

�2�3 �1 0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7 8 9 10

�3�4�5�6 �2 �1 0 1 2 3 4


Precision of MeasurementThe precision of a measurement depends both on your accuracy inmeasuring and the number of divisions on the ruler you use. Supposeyou measured a length of wood to the nearest one-eighth of an inch and got a length of 6 in.

The drawing shows that the actual measurement lies somewhere

between 6 in. and 6 in. This measurement can be written using

the symbol �, which is read plus or minus. It can also be written as acompound inequality.

6 � in. 6 in. � m � 6 in.

In this example, in. is the absolute error. The absolute error is

one-half the smallest unit used in a measurement.

Write each measurement as a compound inequality. Use the variable m.

1. 3 � in. 2. 9.78 � 0.005 cm 3. 2.4 � 0.05 g

4. 28 � ft 5. 15 � 0.5 cm 6. � in.

For each measurement, give the smallest unit used and the absolute error.

7. 12.5 cm � m � 13.5 cm 8. 12 in. � m � 12 in.

9. 56 in. � m � 57 in. 10. 23.05 mm � m � 23.15 mm1�2

1�2

3�8

1�8

1�64

11�16

1�2

1�4

1�2

1�16

11�16

9�16

1�16

5�8

11�16

9�11

5 6 7 8

65–8

5�8

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5

Study Guide and InterventionGraphing Inequalities in Two Variables

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6


Less

on

6-6

Graph Linear Inequalities The solution set of an inequality that involves twovariables is graphed by graphing a related linear equation that forms a boundary of a half-plane. The graph of the ordered pairs that make up the solution set of the inequalityfill a region of the coordinate plane on one side of the half-plane.

Graph y � �3x � 2.

Graph y �3x � 2.Since y � �3x � 2 is the same as y � �3x � 2 and y �3x � 2,the boundary is included in the solution set and the graph should bedrawn as a solid line.Select a point in each half plane and test it. Choose (0, 0) and (�2, �2).

y � �3x � 2 y � �3x � 20 � �3(0) � 2 �2 � �3(�2) � 20 � �2 is false. �2 � 6 � 2

�2 � 4 is true.The half-plane that contains (�2, �2) contains the solution. Shade that half-plane.

Graph each inequality.

1. y � 4 2. x � 1 3. 3x � y

4. �x � y 5. x � y � 1 6. 2x � 3y � 6

7. y � � x � 3 8. 4x � 3y � 6 9. 3x � 6y � 12

x

y

O

x

y

O

x

y

O

1�2

x

y

Ox

y

Ox

y

O

x

y

Ox

y

O

x

y

O

x

y

O

ExampleExample

ExercisesExercises


Solve Real-World Problems When solving real-life inequalities, the domain andrange of the inequality are often restricted to nonnegative numbers or to whole numbers.

BANKING A bank offers 4.5% annual interest on regular savingsaccounts and 6% annual interest on certificates of deposit (CD). If Marjean wantsto earn at least $300 interest per year, how much money should she deposit ineach type of account?

Let x the amount deposited in a regular savings account.Let y the amount deposited in a CD.Then 0.045x � 0.06y � 300 is an open sentence representing this situation.

Solve for y in terms of x.

0.045x � 0.06y � 300 Original inequality

0.06y � �0.045x � 300 Subtract 0.045x from each side.

y � � 0.75x � 5000 Divide each side by 0.06.

Graph y � � 0.75x � 5000 and test the point (0, 0).Since 0 � �0.75(0) � 5000 is false, shade the half-plane that does not contain (0, 0).One solution is (4000, 2000). This represents $4000 deposited at 4.5% and $2,000 deposited at 6%.

1. SOCIAL EVENTS Tickets for the school play cost $5 per student and $7 per adult. The school wants to earn at least $5,400 on each performance.

a. Write an inequality that represents this situation.

b. Graph the solution set.

c. If 500 adult tickets are sold, what is the minimumnumber of student tickets that must be sold?

2. MANUFACTURING An auto parts company can produce 525 four-cylinder engines or270 V-6 engines per day. It wants to produce up to 300,000 engines per year.

a. Write an inequality that represents this situation.

b. Are there restrictions on the domain or range?

3. GEOMETRY The perimeter of a rectangular lot is less than 800 feet. Write aninequality that represents the amount of fencing that will enclose the lot.

Ticket Sales

Student Tickets

Ad

ult

Tic

kets

3000 600 900 x

y

900

600

300

Interest on Accounts

Regular Savings Account ($)C

D A

cco

un

t ($

)

20000 4000 6000 x

y

6000

4000

2000


Graphing Inequalities in Two Variables

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6

ExampleExample

ExercisesExercises

Skills PracticeGraphing Inequalities in Two Variables

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6


Less

on

6-6

Determine which ordered pairs are part of the solution set for each inequality.

1. y � 3x, {(1, 5), (1, 0), (�1, 0), (5, 1)}

2. y � x � 3, {(2, �3), (�2, �1), (1, 6), (3, 4)}

3. y � x � 1, {(3, 1), (�2, �4), (4, �2), (�3, 3)}

Match each inequality with its graph.

4. y � 2x � 2 a. b.

5. y � �3x

6. 2y � x � 4

7. x � y � 1

c. d.


8. y � �1 9. y � x � 5 10. y � 3x

11. y � 2x � 4 12. y � x � 3 13. y � x � 1

x

y

Ox

y

Ox

y

O

x

y

O

x

y

O

x

y

O

x

y

Ox

y

O

x

y

O

x

y

O


Determine which ordered pairs are part of the solution set for each inequality.

1. 3x � y � 6, {(4, 3), (�2, 4), (�5, �3), (3, �3)}

2. y � x � 3, {(6, 3), (�3, 2), (3, �2), (4, 3)}

3. 3x � 2y � 5, {(4, �4), (3, 5), (5, 2), (�3, 4)}

Match each inequality with its graph.

4. 5y � 2x � 10 a. b.

5. 3y � 3x � 9

6. y � 2x � 3

7. x � 2y � �6

c. d.


8. 2y � x � �4 9. 2x � 2y � 8 10. 3y � 2x � 3

11. MOVING A moving van has an interior height of 7 feet (84 inches). You have boxes in12 inch and 15 inch heights, and want to stack them as high as possible to fit. Write aninequality that represents this situation.

BUDGETING For Exercises 12 and 13, use the following information.

Satchi found a used bookstore that sells pre-owned videos and CDs. Videos cost $9 each, andCDs cost $7 each. Satchi can spend no more than $35.

12. Write an inequality that represents this situation.

13. Does Satchi have enough money to buy 2 videos and 3 CDs?

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

Practice Graphing Inequalities in Two Variables

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6

Reading to Learn MathematicsGraphing Inequalities in Two Variables

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6


Less

on

6-6

Pre-Activity How are inequalities used in budgets?


What do 3 and 4 represent in the terms 3x and 4y?

Reading the Lesson

1. Complete the chart to show which type of line is needed for each symbol.

Symbol Type of Line Boundary Part of Solution?

�

�

�

�

2. If a test point results in a false statement, what do you know about the graph?

3. If a test point results in a true statement, what do you know about the graph?

4. When can the origin not be used as a test point?


5. The two-variable inequalities in this lesson can be solved for y in terms of x to get asentence in slope-intercept form. It looks much like a slope-intercept equation, but it hasan inequality symbol instead of an equals sign. For example, 4x � 2y � 5 can be written

as y � �2x � . Explain how to graph an inequality once it is written in slope-intercept

form. Use the idea that greater can mean above and less can mean below.

5�2


Using Equations: Ideal WeightYou can find your ideal weight as follows.

A woman should weigh 100 pounds for the first 5 feet of height and 5 additional pounds for each inch over 5 feet (5 feet 60 inches).A man should weigh 106 pounds for the first 5 feet of height and 6 additional pounds for each inch over 5 feet. These formulas apply topeople with normal bone structures.

To determine your bone structure, wrap your thumb and index fingeraround the wrist of your other hand. If the thumb and finger just touch,you have normal bone structure. If they overlap, you are small-boned.If they don’t overlap, you are large-boned. Small-boned people shoulddecrease their calculated ideal weight by 10%. Large-boned peopleshould increase the value by 10%.

Calculate the ideal weights of these people.

1. woman, 5 ft 4 in., normal-boned 2. man, 5 ft 11 in., large-boned

3. man, 6 ft 5 in., small-boned 4. you, if you are at least 5 ft tall

For Exercises 5–9, use the following information.

Suppose a normal-boned man is x inches tall. If he is at least 5 feettall, then x � 60 represents the number of inches this man is over 5 feet tall. For each of these inches, his ideal weight is increased by 6 pounds. Thus, his proper weight ( y) is given by the formula y 6(x � 60) � 106 or y 6x � 254. If the man is large-boned, theformula becomes y 6x � 254 � 0.10(6x � 254).

5. Write the formula for the weight of a large-boned man in slope-intercept form.

6. Derive the formula for the ideal weight ( y) of a normal-bonedfemale with height x inches. Write the formula in slope-intercept form.

7. Derive the formula in slope-intercept form for the ideal weight ( y)of a large-boned female with height x inches.

8. Derive the formula in slope-intercept form for the ideal weight ( y)of a small-boned male with height x inches.

9. Find the heights at which normal-boned males and large-bonedfemales would weigh the same.

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6

Chapter 6 Test, Form 1

NAME DATE PERIOD

SCORE


Ass

essm

ent

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–9, solve each inequality.

1. x � 7 � 3A. {x � x � 10} B. {x � x � �4} C. {x � x � 10} D. {x � x � �4} 1.

2. 3 � t � 1A. {t � t � 4} B. {t � t � 2} C. {t � t � 2} D. {t � t � 4} 2.

3. 17 � a � 7A. {a � a � 10} B. {a � a � �10} C. {a � a � 24} D. {a � a � �24} 3.

4. 3 � �5c

�

A. �c � c � �35�� B. �c � c � �

35�� C. {c � c � 15} D. {c � c � 15} 4.

5. 1 � ��4y�

A. �y � y � ��14�� B. {y � y � �4} C. {y � y � 4} D. {y � y � 3} 5.

6. 5s � �25A. {s � s � 125} B. {s � s � �125} C. {s � s � �5} D. {s � s � �5} 6.

7. �36 � 3tA. {t � t � �12} B. {t � t � 12} C. {t � t � 12} D. {t � t � �12} 7.

8. 6y � 8 � 4y � 26A. {y � y � �9} B. {y � y � �17} C. {y � y � 9} D. {y � y � 17} 8.

9. 3(2d � 1) � 4(2d � 3) � 3A. {d � d � �9} B. {d � d � �6} C. {d � d � 3} D. {d � d � 6} 9.

10. Six is at least four more than a number. Which inequality represents this sentence?A. 6 � n � 4 B. 6 � n � 4 C. 4 � n � 6 D. 4 � n � 6 10.

11. Which of the following is the graph of the solution set of m � �1 and m � 1?A. B.

C. D. 11.

12. Which compound inequality has the solution set shown in the graph?

A. �3 � n � 1 B. �3 � n � 1 C. �3 � n � 1 D. �3 � n � 1 12.

�1�2�3�4 0 1 2 43

�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43

�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43

66


Chapter 6 Test, Form 1 (continued)


A. x � �1 or x � 3 B. x � �1 or x � 3C. x � �1 or x � 3 D. x � �1 or x � 3 13.

14. Which of the following is the solution set of 2s � 1 � 9 or s � �1?A. {s � s � �1 or s � 4} B. {s � s � �1 or s � 4}C. {s � �1 � s � 4} D. {s � s � �1 or s � 5} 14.

15. Which of the following is the solution set of � s � 6 � 12?A. {6, �18} B. {�6} C. {18} D. {�6, 18} 15.

16. Solve � 1 � 2b � 1.A. {1, �1} B. {�1, 0} C. {0, 1} D. {0} 16.

17. Solve � x � 3 � � 2.A. {x � 1 � x � 5} B. {x � �5 � x � �1}C. {x � �1 � x � 1} D. {x � �1 � x � 5} 17.

18. Which inequality has the solution set shown in the graph? A. y � 1 B. y � 1C. y � 1 D. y � 1 18.

19. Which inequality has the solution set shown in the graph?A. y � �x � 2 B. y � �x � 2C. y � �x � 1 D. y � �x � 1 19.

20. Juan’s income y consists of at least $37,500 salary plus 5% commission on all of his sales x. Which inequality represents Juan’s income in one year?A. y � 37,500 � 5x B. y � 37,500 � 0.05xC. y � x � 0.05(37,500) D. y � 37,500 � 5 20.

Bonus If x � 0, which integer does not satisfy the inequality B:x � 2 � 1?

�1�2�3�4 0 1 2 43

NAME DATE PERIOD

66

y

xO

y

xO

(0, 2)

(2, 0)

Chapter 6 Test, Form 2A

NAME DATE PERIOD

SCORE


Ass

essm

ent



1. �51 � x � 38A. {x � x � �13} B. {x � x � 89} C. {x � x � �89} D. {x � x � �13} 1.

2. m � �38� � �

12�

A. �m � m � �78�� B. �m � m � �

78�� C. �m � m � �

18�� D. �m � m � �

18�� 2.

3. 6n � 19 � 5n

A. {n � n � �19} B. {n � n � 19} C. {n � n � 19} D. �n � n � �1191�� 3.

4. ��t2�

� 4

A. {t � t � �8} B. {t � t � �2} C. {t � t � 2} D. {t � t � �8} 4.

5. �154�

� ��27�d

A. �d � d � �54�� B. �d � d � �

54�� C. �d � d � ��

54�� D. �d � d � ��

54�� 5.

6. �3.5z � 42A. {z � z � 12} B. {z � z � 12} C. {z � z � �12} D. {z � z � �12} 6.

7. 4w � 6 � 6w � 20A. {w � w � 7} B. {w � w � 2} C. {w � w � �7} D. {w � w � �2} 7.

8. 2v � 3 � �5v

4� 8�

A. �v � v � 1�23�� B. �v � v � �1�

13�� C. �v � v � 1�

23�� D. �v � v � �1�

13�� 8.

9. 8r � (5r � 4) � �31A. {r � r � �9} B. {r � r � �9} C. {r � r � 9} D. {r � r � 9} 9.

10. The sum of two consecutive integers is at most 3. What is the greatest possible value for the greater integer?A. 5 B. 1 C. 3 D. 2 10.

11. Which of the following is the graph of the solution set of y � �3 or y � 1? A. B.

C. D. 11.�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43

�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43

66


Chapter 6 Test, Form 2A (continued)


A. �1 � n � 2 B. �1 � n � 2C. n � �1 or n � 2 D. �1 � n � 2 12.

13. Which of the following is the solution set of �4 � 3t � 5 � 20?A. {t ��3 � t � 5} B. {t � t � �3}C. {t � t � �3 and t � 5} D. {t � t � �3 or t � 5} 13.

14. Which of the following is the graph of the solution set of t � 4 � 4t � 8 or 3t � 14 � 4t?A. B.

C. D. 14.

15. Which of the following is the solution set of � 3x � 18 � 12?A. {2} B. {2, 10} C. {�10, �2} D. {10} 15.

16. The graph below represents the solution set of which inequality?

A. � w � 5 � � 3 B. � w � 5 � � 3C. � w � 5 � � 3 D. � w � 5 � � 3 16.

17. Which of the following is the solution set of � 2x � 3 � � 4?

A. �x � x � ��12� or x > �

72�� B. {x � x � �1 or x � 7}

C. �x � ��12� � x � �

72�� D. �x � x � �

12� or x � �

72�� 17.

18. Which ordered pair is part of the solution set of the inequality 12 � y � �3x?A. (�16, 3) B. (1, 4) C. (4, �1) D. (3, �16) 18.

19. Which inequality is graphed at the right?A. y � 2x � 1 B. y � 2x � 1

C. y � �12�x � 1 D. y � �

12�x � 1 19.

20. Taka is planning to buy a new coat and new shoes.He has saved $122. Which inequality represents this situation if x represents the cost of a coat and y represents the cost of the shoes he buys?A. 122 � y � x B. y � 122 � xC. y � x � 122 D. y � 122 � x 20.

Bonus Solve 6(� n � � 3) � 4� n � � 5 11. B:

0 1 2 4 5 6 7 83

�1�2�3�4�5 0 1 2 3�1�2�3�4�5 0 1 2 3

�1�2�3�4�5 0 1 2 3�1�2�3�4�5 0 1 2 3

�1�2�3�4 0 1 2 43

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y

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(0, 1) (2, 2)

Chapter 6 Test, Form 2B

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1. �13 � w � 12A. {w � w � �25} B. {w � w � �25} C. {w � w � �1} D. {w � w � �1} 1.

2. x � �14� � ��

12�

A. �x � x � ��14�� B. �x � x � ��

34�� C. �x � x � ��

14�� D. �x � x � ��

34�� 2.

3. 2x � 7 � 3x

A. �x � x � �57�� B. {x � x � �7} C. {x � x � 7} D. {x � x � �7} 3.

4. ��m

5�� 3

A. {m � m � �15} B. {m � m � �15} C. {m � m � 15} D. {m � m � 15} 4.

5. ��23�s � 6

A. {s � s � �9} B. {s � s � 9} C. {s � s � 9} D. {s � s � �9} 5.

6. �1.1t � 4.62A. {t � t � 5.72} B. {t � t � 5.72} C. {t � t � �4.2} D. {t � t � �4.2} 6.

7. 5z � 4 � 2z � 8A. {z � z � 4} B. {z � z � 1} C. {z � z � 4} D. {z � z � 1} 7.

8. �2 �

24b� � 3b � 6

A. {b � b � �5} B. {b � b � �5} C. {b � b � �2} D. {b � b � �2} 8.

9. 7 � 9r � (r � 12) � 25

A. {r � r � �3} B. �r � r � ��35�� C. {r � r � �3} D. �r � r � ��

35�� 9.

10. The sum of two consecutive integers is at most 7. What is the largest possible value for the lesser integer?A. 1 B. 3 C. 2 D. 5 10.

11. Which of the following is the graph of the solution set of x � 0 or x � �4?A. B.

C. D. 11.�1�2�3�4�5�6 0 1 2�1�2�3�4�5�6 0 1 2

�1�2�3�4�5�6 0 1 2�1�2�3�4�5�6 0 1 2

66


Chapter 6 Test, Form 2B (continued)


A. �2 � y � 3 B. �2 � y � 3C. y � �2 or y � 3 D. �2 � y � 3 12.

13. Which of the following is the solution set of �3 � 2x � 7 � 13?A. {x � �5 � x � 3} B. {x � x � �5}C. {x � x � 3 or x � �5} D. {x � �5 � x � 3} 13.

14. Which of the following is the graph of the solution set of 7a � 3 � a � 15 or 5a � 3 � 8a?A. B.

C. D. 14.

15. Which of the following is the solution set of � 2x � 5 � 9?A. {�7, 2} B. {�7} C. {2} D. {�2, 7} 15.

16. The graph below represents the solution set of which inequality?

A. � 5x � 10 � � 10 B. � 5x � 10 � � 10C. � 5x � 10 � � 10 D. � 5x � 10 � � 10 16.

17. Which of the following is the solution set of � 4 � 7x � � 3?

A. �x � x � �17� or x � 1� B. {x � x is a real number}

C. �x � x � �17� or x � 1� D. {x � 1 � x � 7} 17.

18. Which ordered pair is part of the solution set of the inequality 5 � y � �3x?A. (2, �1) B. (�2, �1) C. (�3, �5) D. (3, �5) 18.

19. Which inequality is graphed?A. y � 2x � 1 B. y � �2x � 1C. y � 2x � 1 D. y � �2x � 1 19.

20. Alicia is planning to buy a new baseball glove and a new baseball bat with at most $196.Which inequality represents this situation if xrepresents the cost of a glove and y represents the cost of the bat she buys?A. y � 196 � x B. y � 196 � xC. 196 � y � x D. y � x � 196 20.

Bonus Solve 2 � 3x � 5(2 � x) � 3(2 � x) � 10. B:

�1�2 0 1 2 4 5 63

�1�2�3�4 0 1 2 43�1�2�3�4�5�6 0 1 2

�1�2�3�4�5�6 0 1 2�1�2�3�4�5�6 0 1 2

�1�2�3�4 0 1 2 43

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y

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(�1, 1)

(0, �1)

Chapter 6 Test, Form 2C


Solve each inequality. Then graph your solution on a number line.

1. x � 12 � 1 1.

2. �14 � n � 5 2.

For Questions 3 and 4, solve each inequality.

3. 4 � �2 � t 3.

4. 7 � z � 3 4.

5. Define a variable, write an inequality, and solve: 5.The sum of 2 and a number is no greater than 7.

Solve each inequality.

6. �b8� � ��

15� 6.

7. �6t� � 14 7.

8. �19.8 � 3.6y 8.

9. �4r � 22 9.

10. �2a

5� 7� � 5 10.

11. 4x � 5 � 2x � 11 11.

12. 5( p � 2) � 2( p � 1) � 7p � 4 12.

13. 1.3(c � 4) � 2.6 � 0.7c 13.

For Questions 14–17, solve each compound inequality.Then graph the solution set.

14. 3w � 6 and �5 � w 14.

15. �4 � n or 3n � 1 � �2 15.

16. �1 � �3b

2� 4� � �

225� 16.

17. �4x � 8 � �4 or 7x � 5 � 16 17.

�1�2�3�4 0 1 2 43

�2 0 2 4 86

0

�1�2�3�4�5�6 0 1 2

�17�19�21 �15

131211109 14 15 1716

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Chapter 6 Test, Form 2C (continued)

18. Define a variable, write an inequality and solve. Felicita’s 18.bank charges $2.50 per month plus $0.10 per check. How many checks does she write if her bank charges are always between $3.50 and $5.00?


19. � 1 � y � 2 19.

20. � 3 � 2x � � 1 20.

Solve each open sentence.

21. � 8x � 2 � 14 21.

22. � 3w � 1 � � 8 22.

For Questions 22 and 23, graph each inequality.

23. y � ��13�x � 2 23.

24. 2x � 3y � 12 24.

25. EXPENSES Camille has no more than $20.00 to spend each 25.week for lunch and bus fare. Lunch costs $3.00 each day, and bus fare is $0.75 each ride. Write an inequality for this situation. Can Camille buy lunch 5 times and ride the bus 8 times in one week?

Bonus Graph the solution set of the compound inequality B:3 � � x � 4 � � 7.

y

xO

y

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�1�2�3�4 0 1 2 43

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Chapter 6 Test, Form 2D



1. y � 7 � 5 1.

2. m � 6 � �3 2.

For Questions 3 and 4, solve each inequality.

3. 3 � s � 6 3.

4. 8 � k � 13 4.

5. Define a variable, write an inequality, and solve: 5.14 is greater than a number plus 5.


6. �h3� � 9 6.

7. ��23� � �5

z� 7.

8. 9.8 � 2.8k 8.

9. �3m � �18 9.

10. �3 �

24f

� � 1 10.

11. 5t � 8 � 3t � 3 11.

12. 3(�w � 6) � 2(2w � 8) � 1 12.

13. 1.9 � 1.7x � 2.1(3 � x) 13.

For Questions 14–17, solve each compound inequality.Then graph the solution set.

14. 7w � 14 and w � 3 14.

15. �w3� � 1 or 3w � 5 � 11 15.

16. 1 � �2y

4� 3� � �

141� 16.

17. 2 � 3x � 8 or 4 � 7x � �17 17.

�1�2�3�4 0 1 2 43

�1�2 0 1 2 4 5 63

0

�1�2�3�4 0 1 2 43

�7�9�11 �5

1312111098 14 15 16

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Chapter 6 Test, Form 2D (continued)

18. Define a variable, write an inequality and solve. Jose’s bank 18.charges $3.75 per month plus $0.10 per check. How many checks does he write if his bank charges are always between $5.75 and $7.25?


19. � z � 4 � 7 19.

20. � w � 1 � � 4 20.

Solve each open sentence.

21. � 2x � 5 � 3 21.

22. � 4 � 3c � � 5 22.


23. y � 3x 23.

24. 2y � 4x � 8 24.

25. SHOPPING Matthew is shopping for shoes and socks. He 25.has $75.00 to spend. The shoes he likes cost $28.00, and the socks cost $4.00. Write an inequality for this situation. Can Matthew buy 2 pairs of shoes and 5 pairs of socks?

Bonus Graph the solution set of the compound inequality B:� x � 1 � � 4 or � x � 1 � � 6.

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y

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�1�2�3 0 1 2 4 53

�11 30

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Chapter 6 Test, Form 3



1. m � (�3.4) � 12.7 1.

2. t � (�4) � 32 2.

Define a variable, write an inequality, and solve each problem.

3. Negative three sevenths plus a number is at least 2. 3.

4. A number less 15 is greater than the sum of twice the 4.number and 8.


5. �2.6 � �w4� 5.

6. �11t � �9 6.

7. 2 � 3b � �11 �

715b� 7.

8. 5x � 3(x � 6) � 0 8.

9. �3x � 2(6x � 7) � 4(3 � 2x) � 17x � 8 9.


10. Raul plans to spend $78.00 on two shirts and a pair of 10.jeans. He bought the two shirts for $19.89 each. How much can he spend on the jeans?

11. The sum of two consecutive positive even integers is at 11.most 15. What are the possible pairs of integers?

12. Susan makes 10% commission on her sales. She also 12.receives a salary of $25,600. How much must she sell to receive a total income between $32,500 and $41,900?

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Chapter 6 Test, Form 3 (continued)

Solve each compound inequality, and graph the solution set.

13. 6 � 4m � 10 and 4(m � 2) � 6 � 3m 13.

14. ��n2� � 3 or 2n � 3 � 12 14.

15. 2(x � 14) � x � 7(x � 2) � x � x � 70 15.

For Questions 16–18, solve each open sentence. Then graph the solution set.

16. � 5x � 3 � � 17 16.

17. ��4x � 8 � � 16 17.

18. � �3 �

52x

� � 1 18.

19. Graph �y � 3x. 19.

20. DOGS Each afternoon Maria walks the dogs at a local pet 20.shelter for up to 2 hours. Maria spends 16 minutes walking a large dog and 12 minutes walking a small dog. Write an inequality for this situation. If Maria walked 9 dogs in one afternoon, what is the greatest number of large dogs that she could have walked that afternoon?

Bonus If xy � 0, determine if the compound inequality, B:2x � 1 � 7 and 4 � y � 3, is true or false.Explain your reasoning.

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Chapter 6 Open-Ended Assessment


Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.

1. Solve 10n � 7(n � 2) � 5n � 12. Explain each step in yoursolution.

2. Draw a line on a coordinate plane so that you can determine atleast two points on the graph.a. Write an inequality to represent one of the half planes created

by the line.b. Determine if the solution set of the inequality written for part

a includes the line or not. Explain your response.

3. Let b � 2. Describe how you would determine if ab � 2a.

4. a. Explain why the solution set for � x � � 3 is {�3, 3}.b. Determine if the open sentence � x � 2 � � 4 and the compound

inequality �2x � 4 or x � 6 have the same solution set.

5. ARCHITECTURE An architect is designing a house for theFrazier family. In the design, she must consider the desires of thefamily and the local building codes. The rectangular lot on whichthe house will be built is 158 feet long, and 90 feet wide.a. The building codes state that one can build no closer than

20 feet to the lot line. Write an inequality to represent thepossible widths of the house along the 90-foot dimension. Solvethe inequality.

b. The Fraziers requested that the rectangular house contain noless than 2800 square feet and no more than 3200 square feetof floor space. If the house has only one floor, use themaximum value for the width of the house from part a, andexplain how to use an inequality to find the possible lengths.

c. The Fraziers have asked that the cost of the house be about$175,000 and are willing to deviate from this price no morethan $20,000. Write an open sentence involving an absolutevalue and solve. Explain the meaning of the answer.

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Chapter 6 Vocabulary Test/Review

Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.

1. The Addition Property of Inequalities states that if the 1.same number is added to each side of a true inequality,the resulting inequality is true.

2. An inequality defines the boundary or edge for each 2.half-plane.

3. A compound inequality containing and is true if one or both 3.of the inequalities is true.

4. According to the Division Property of Inequalities, if each 4.side of a true inequality is divided by the same positivenumber, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.

5. The solution set for an inequality that contains two 5.variables consists of many ordered pairs which fill a region on the coordinate plane called a half-plane.

6. The graph of a compound inequality containing and is the 6.intersection of the graphs of the two inequalities.

7. The Division Property of Inequalities states that if each 7.side of a true inequality is divided by the same negativenumber, the resulting inequality is also true.

8. Set-builder notation is a way of writing a solution set. 8.

9. If the same number is subtracted from each side of a true 9.inequality, the resulting inequality is also true.

10. The graph of a compound inequality containing and is the 10.union of the graphs of the two inequalities.

In your own words—

11. Explain how to use the Multiplication Property of Inequalities

to solve the inequality ��23�x � 7.

Addition Property of Inequalities

boundarycompound inequality

Division Property of Inequalities

half-planeintersection

Multiplication Property of Inequalities

set-builder notation

Subtraction Property of Inequalities

union

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Chapter 6 Quiz (Lessons 6–1 and 6–2)

66



1. n � 11 � 3 1.

2. w � 9 � �5 2.

For Questions 3 and 4, solve each inequality. 3.

3. � 4 � �4 � r 4. �14� � m �

34� 4.

5. Define a variable, write an inequality, and solve: 5.A number decreased by 7 is at least 15.

Solve each inequality.6. �1

m3�

� �6 7. ��49� � ��1

52�

r 6.

7.

8. �3n � 84 9. �3.22 1.4w 8.

9.10. STANDARDIZED TEST PRACTICE Which inequality does not

have the solution {x � x � �2}?

A. �3x � 6 B. ��2x

� � 1

C. 7x � �14 D. �43�x � ��

83� 10.

13121110 14 15 17 1816

13121110 14 15 17 1816

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Chapter 6 Quiz (Lesson 6–3)


1. ��d5� � 12 8 1.

2. 9y � 6 � 2y � 15 2.

3. 3(y � 2) � 4(3 � 2y) � 6(3y � 1) � 11y 3.

4. 23 � t � 2(t � 9) � 3(t � 2) 4.

5. Define a variable, write an inequality, and solve. The sum 5.of a number and three is less than nineteen less the number.

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1. Solve �14 � 3x � 1 � 1. Then graph the solution set. 1.

2. Solve the compound inequality 2y � 3 � 7 or �3y � �18. 2.Then graph the solution set.

3. Define a variable, write an inequality and solve. 3.Eight times a number is between 16 and 40.

4. Solve � 2x � 5 � � 3. 4.

5. Write an open sentence involving absolute value for this 5.graph.

�1�2�3�4 0 1 2 43

0 1 2 4 5 6 7 83

�1�2�3�4�5�6 0 1 2

Chapter 6 Quiz (Lesson 6–6)

1. From the set {(0, 1), (3, �3), (4, 2), (�1, 2)}, which ordered 1.pairs are part of the solution set for x � y � 0?


2. x � 3 2.

3. �2(x � y) � 4 3.

4. CLOTHING Rita plans to spend at most $230.00 on a new 4.wardrobe. The skirts she wants to buy cost $35 each, and the blouses cost $25 each. Write an inequality that represents the number of skirts and blouses Rita can buy. Can Rita buy 4 skirts and 4 blouses?

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Chapter 6 Quiz (Lessons 6–4 and 6–5)

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Chapter 6 Mid-Chapter Test (Lessons 6–1 through 6–3)




1. r � �78� � 1

A. �r � r � �18�� B. �r � r � �

18�� C. �r � r � 1�

78�� D. �r � r � 1�

78�� 1.

2. 12x � 5 17x � 10A. {x � x � �3} B. {x � x 3} C. {x � x �3} D. {x � x � 3} 2.

3. 6m � 2(7 � 3m) � 5(2m � 3) � m

A. {m � m � 1} B. �m � m � �19�� C. {m � m � 1} D. �m � m � �

19�� 3.

4. Four less than three times a number is at most five.Which of the following describes the number?A. any number less than 3B. any number greater or equal to 3C. any number less than or equal to 3

D. any number less than or equal to �13� 4.

Solve and check each inequality.

5. 4.2 � �11 � t 5.

6. ��35�v � ��1

45�

6.


7. For a package to qualify for a certain postage rate, the 7.sum of its length and girth cannot exceed 85 inches.If the girth is 63 inches, how long can the package be?

8. The minimum daily requirement of vitamin C for 8.14-year-olds is at least 50 mg per day. An average-sized apple contains 6 mg of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?

Part II

Part I

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Chapter 6 Cumulative Review (Chapters 1–6)

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1. Simplify 4(2y � 5) � 6(4y � 3). (Lesson 1–6) 1.

2. Name the set or sets of numbers to which the real number 2.0 belongs. (Lesson 2–7)

3. Solve 3x � �23�. (Lesson 3–3) 3.

4. State whether the percent of change is a percent of increase 4.or a percent of decrease. Then find the percent of change.(Lesson 3–7)

original: 76new: 57

5. Express the relation {(�2, 1), (3, �1), (2,�2), (�2, 0)} as a 5.mapping. Then write the inverse of the relation. (Lesson 4–3)

6. Determine whether the sequence �6, �3, 0, 3 … is an 6.arithmetic sequence. If it is, state the common difference.(Lesson 4–7)

7. Find the slope of the line that passes through (�2, 0) and 7.(5, �8). (Lesson 5–1)

8. The Lopez family drove 165 miles in 3 hours. Write a direct 8.variation equation for the distance driven in any time. How far can the Lopez family drive in 5 hours? (Lesson 5–2)

9. Write an equation of a line that passes through (�2, �1) 9.with slope 3. (Lesson 5–4)

10. Draw a scatter plot of the relation, and determine what 10.relationship exists, if any, in the data. (Lesson 5–7)

{(1, 5), (1, 8), (2, 7), (3, 5), (3, 8), (4, 4), (5, 3), (5, 5),(6, 2), (7, 4), (8, 1), (9, 2)}

11. Solve 12 � r � 15. Then graph the solution. (Lesson 6–1) 11.

12. Solve �2u �7

15� 3. (Lesson 6–3) 12.

13. Define a variable, write a compound inequality, and solve 13.the problem. (Lesson 6–4)

Seven less than twice a number is greater than 13 or less than or equal to �5.

14. Solve �3x � 4� � 5. Then graph the solution set. (Lesson 6–5) 14.

�1�2�3�4 0 1 2 43

�1�2�3�4 0 1 2 43

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2 3 4 5 6 7 8 9

X Y

Standardized Test Practice (Chapters 1–6)


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1. Evaluate [1 � 4(5)] � [3(9) � 7]. (Lesson 1–2)

A. 45 B. 27 C. 41 D. 31 1.

2. If a person’s birthday is in January, what are the odds that it is between the 20th and the 29th, inclusively? (Lesson 2–6)

E. �1301�

F. �281�

G. �2311�

H. �1201�

2.

3. How many liters of a 10% saline solution must be added to 4 liters of a 40% saline solution to obtain a 15% saline solution? (Lesson 3–9)

A. 20 L B. 4 L C. 2 L D. 48 L 3.

4. The currency exchange rate between the U.S. and Canada in 1999 could be modeled by the equation d � 1.49c where d represents the number of U.S. dollars and c represents the number of Canadian dollars. Solve the equation for Canadian dollar amounts of $1, $2,$5, and $20. (Lesson 4–4)

E. {(1, 1.49), (2, 2.98), (5, 7.45), (20, 29.8)F. {(1, 1.5), (2, 3), (5, 7.5), (20, 30)}G. {(1, 0.67), (2, 1.34), (5, 3.36), (20, 13.42)}H. {(1, 2.49), (2, 3.49), (5, 6.49), (20, 21.49)} 4.

5. If a line passes through (0, �6) and has a slope of �3, what is the equation of the line? (Lesson 5–3)

A. y � �6x � 3 B. x � �6y � 3 C. y � �3x � 6 D. x � �3y � 6 5.

6. If r is the slope of a line, and s is the slope of a line perpendicular to that line, what is the relationship between r and s? (Lesson 5–6)

E. There is no relationship. F. r � s

G. r � �s H. r � ��1s� 6.

7. Which inequality does not have the solution {t � t � 4}? (Lesson 6–2)

A. �t � �4 B. 3t � 12 C. �2t� � 2 D. ��8

t� � ��

12� 7.

8. Solve 4 � 2r 3(5 � r) � 7(r � 1). (Lesson 6–3)

E. �r � r � ��32�� F. {r � r � �3} G. {r � r � �2} H. �r � r � ��

94�� 8.

9. Write a compound inequality for the graph. (Lesson 6–4)

A. x � �1 and x 2 B. x � �1 or x 2C. x � �1 or x � 2 D. x � �1 and x � 2 9. DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

Part I: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

�1�2�3�4 0 1 2 43


Standardized Test Practice (continued)

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10. Find the 13th term of the arithmetic sequence 10. 11.

�12�, �

34�, 1, 1�

14�, 1�

12�, ... . (Lesson 4–7)

11. If y � 18 when x � 16, find y when x � 6.(Lesson 5–2)

For Questions 12 and 13, determine the value that is missing.

12. The solution set is {n � n 15} for the 12. 13.inequality n � 7 ___. (Lesson 6–1)

13. If � a � 8 � � 17, then a � ___ or a � �9.(Lesson 6–5)

Column A Column B

14. 14.

(Lesson 3–7)

15. 15.

(Lesson 5–6)

16. �3 � 2x � 1 � 7 16.

(Lesson 6–4)

�2x

�4x

DCBA

DCBAThe slope of any line

perpendicular to y � 4x � 3.The slope of the line

y � 4x � 3.

DCBAthe percent of change if

original: 40 new: 50the percent of change if

original: 35 new: 49

Part 3: Quantitative Comparison

Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.

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A

D

C

B

Part 2: Grid In

Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.

First Semester Test (Chapters 1–6)

NAME DATE PERIOD

SCORE


For Questions 1–20, write the letter for the correct answer in the blank at the right of each question.

1. Evaluate 4v2 � (n2 � 3s) if n � 8, s � 4, and v � 7.A. 120 B. 732 C. 32 D. 144 1.

2. Simplify 9a2 � 7a � 4a2 � 2a.A. 13a2 � 9a B. 22a3 C. 36a2 � 14a D. 16a2 � 6a 2.

3. Identify the conclusion of the statement.If the oven works properly, then we will learn how to cook.A. The oven works properly. B. The oven is new.C. I already know how to cook. D. We will learn how to cook. 3.

4. Evaluate � x � 2 � � �34� if x � �

151�.

A. �9290�

B. �5210�

C. �1290�

D. ��2101� 4.

5. The land areas in square miles of the 19 zip codes in Guam are listed below.Use a stem-and-leaf plot to determine which measure of central tendency is equal to 7.1 1 10 6 9 6 30 6 6 19 10 6 2 7 17 1 17 35 20A. mean B. median C. mode D. frequency 5.

6. Name the set of numbers to which the real number �196� does not belong.A. rational number B. integerC. irrational number D. natural number 6.

7. Translate the sentence into an equation. Twelve times a number r is the same as two times the sum of r and p.A. 12r � 2(r � p) B. 12r � 2r � pC. 12 � r � 2(r � p) D. 12 � r � 2r � p 7.

8. Solve �56�h � �30.

A. �25 B. �180 C. �150 D. �36 8.

9. Solve 5(a � 12) � 8(3a � 2).

A. ��1149�

B. �4 C. 3 D. ��4249�

9.

10. The surface area A of a sphere is A � 4�r2 where r is the radius of the sphere. What is the radius, rounded to the nearest tenth, of a ball with surface area equal to 85 square inches?A. 2.6 in. B. 6.8 in. C. 2.7 in. D. 6.7 in. 10.

Ass

essm

ent


First Semester Test (continued)(Chapters 1–6)

11. The coordinates of the vertices of rectangle MNOP are M(�2, 1), N(4, 3),O(5, 0), and P(�1, �2). If the rectangle is reflected over the x-axis, which point below has the correct coordinates?A. M(2, 1) B. N(4, �3) C. O(�5, 0) D. P(�2, �1) 11.

12. The graph of the line is the graph of which equation?A. 3x � 2y � 12 B. 3x � 2y � 12C. 3x � 2y � �12 D. 3x � 2y � �12 12.

13. If f(x) � 4x � 5, find f(3a � 1).A. 12a � 4 B. 7a � 4C. 12a � 1 D. 12a � 4x � 5 13.

14. The average rate of change for the combined population of San Diego,California and Tijuana, Mexico was 0.0825 million people per year from 1990 to 2000. If the 2000 population was about 4 million, what was the approximate 1990 population? Source: Time Magazine

A. 4.25 million B. 3.9 million C. 3.175 million D. 1.4 million 14.

15. A line passes through (�1, 3) and (1, �3). Which equation does notrepresent the line?A. (y � 3) � �3(x � 1) B. 3x � y � 0C. (y � 3) � �3(x � 1) D. y � �3x 15.

16. Write the slope-intercept form of an equation for the line that passes through (4, 0) and is parallel to the graph of 3y � 6x � 4.A. y � 2x � 8 B. 2y � �x C. y � 2x � 4 D. y � �2x � 8 16.

17. Solve 8r � 14 � 12r � 6.A. {r � r � �2} B. {r � r � 2} C. {r � r � 2} D. {r � r � �2} 17.

18. Solve 8 � 2h � 6 � 22.A. {h� 4 � h � 11} B. {h� 7 � h � 14}C. {h� 1 � h � 8} D. {h� 0 � h � 14} 18.

19. Which graph represents the solution of � n � 5 � � 1?A. B.

C. D. 19.

20. Which ordered pair is not a solution of 4x � 8y 24?A. (2, �2) B. (�5, �4) C. (7, �1) D. (�8, �8) 20.

�4�3�2�1 0 2 3 4 5 6 71�1 0 1 2 3 4 5 6 7 8 9 10

�9�8�7�6�5�4�3�2�1 0 21�1�2�3�5�6 �4 0 1 2 3 4 5

NAME DATE PERIOD

y

xO



21. Evaluate �3abc� c2� if a � 14, b � 3, and c � 7. 21.

22. Find the solution set for 18 � 3x 9 if the replacement set 22.is {1, 2, 3, 4, 5, 6}.

23. Name the property used in the equation n � 5 � 0. Then 23.find the value of n.

24. Simplify 4.1(x � 2y) � 2.7(x � y) � 5x. 24.

25. Find a counterexample for the statement. If you visit an 25.art gallery, then you will see a painting by Monet.

26. Name the coordinates of the 26.points graphed on the number line.

27. Simplify 4x( � 7y) � (5u)(3v) � 11uv. 27.

28. Evaluate �uv �w

12� if u � 3.6, v � 4, and w � 6. 28.

29. A card is selected at random from a standard deck of 29.52 cards. What are the odds against selecting a heart?

30. Solve the following problem by working backward. A father 30.made a batch of cookies. His son ate four and gave six to a friend. Two of his daughters ate half of the remaining cookies. The father was left with thirteen cookies. How many cookies did the father make?

For Questions 31 and 32, solve each equation. 31.

31. �m6� � �

168� 32. 2(3y � 2) � y 32.

33. State whether the percent of change is a percent of increase 33.or a percent of decrease. Then find the percent of change.original: 180new: 207

34. Two airplanes leave Phoenix at the same time and fly in 34.opposite directions. One plane travels 60 miles per hour

faster than the other. After 2�12� hours they are 1700 miles

apart. What is the rate of the slower plane?

35. Identify the transformation as a reflection, 35.translation, dilation, or rotation.

NAME DATE PERIOD

�4�5 �3�2�1 0 2 3 4 5 61

Ass

essm

ent



36. Express the relation shown in the 36.graph as a set of ordered pairs. Then write the inverse of the relation.

37. Graph y � 2x � 3. 37.

38. Write an equation for the nth term of the arithmetic 38.sequence 7, 11, 15, 19, … .

39. Ms. Ortiz paid $38 for 20 gallons of gasoline. Write a direct 39.variation equation relating the cost of gasoline C to the number of gallons purchased n.

40. Find the slope, y-intercept, and x-intercept of the line 40.represented by the equation 3x � 4y � 8.

41. Find the value of r so that the line through (2, 3) and (r, �3) 41.

has a slope perpendicular to the graph of y � ��16�x � 3.

For Questions 42 and 43, use the table that shows UV indices and humidities for 6 cities on a July day.

42. Use a scatter plot to determine what relationship, if any, 42.exists in the data.

43. Write the slope-intercept form of an equation for a line of 43.fit.

For Questions 44 and 45, solve each inequality. 44.

44. �5t

2� 9� � 4t 45. 2(5x � 4) 7(x � 2) 45.

46. Solve 4x � 9 � 1 or 3x 15. Then graph the solution set. 46.

47. Solve � 2u � 7 � � 13. 47.

�4�3�2�1 0 2 3 4 5 6 71

y

xO

NAME DATE PERIOD

y

xO

UV Index 4 4 6 7 8 10

Humidity Forecast (Percent) 74 80 63 52 55 29

Standardized Test PracticeStudent Record Sheet (Use with pages 364–365 of the Student Edition.)

© Glencoe/McGraw-Hill A1 Glencoe Algebra 1

Select the best answer from the choices given and fill in the corresponding oval.

1 4 7

2 5 8

3 6 9

Solve the problem and write your answer in the blank.

For Questions 11 and 15, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.

10 11 15

11 (grid in)

12

13

14

15 (grid in)

16

17

18

Record your answers for Questions 19–21 on the back of this paper.

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NAME DATE PERIOD

66

An

swer

s

Part 2 Short Response/Grid InPart 2 Short Response/Grid In

Part 3 Extended ResponsePart 3 Extended Response

Part 1 Multiple ChoicePart 1 Multiple Choice


Stu

dy G

uid

e a

nd I

nte

rven

tion

So

lvin

g In

equ

alit

ies

by A

ddit

ion

an

d S

ub

trac

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-1

6-1

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Lesson 6-1

Solv

e In

equ

alit

ies

by

Ad

dit

ion

Add

itio

n c

an b

e u

sed

to s

olve

in

equ

alit

ies.

If a

ny

nu

mbe

r is

add

ed t

o ea

ch s

ide

of a

tru

e in

equ

alit

y,th

e re

sult

ing

ineq

ual

ity

is a

lso

tru

e.

Ad

dit

ion

Pro

per

ty o

f In

equ

alit

ies

For

all

num

bers

a,

b, a

nd c

, if

a�

b, t

hen

a�

c�

b�

c,

and

if a

�b,

the

n a

�c

�b

�c.

Th

e pr

oper

ty i

s al

so t

rue

wh

en �

and

�ar

e re

plac

ed w

ith

�an

d �

.

Sol

ve x

�8

��

6.T

hen

gra

ph

it

on a

nu

mb

er l

ine.

x�

8 �

�6

Orig

inal

ineq

ualit

y

x�

8 �

8 �

�6

�8

Add

8 t

o ea

ch s

ide.

x�

2S

impl

ify.

Th

e so

luti

on i

n s

et-b

uil

der

not

atio

n i

s {x

|x�

2}.

Nu

mbe

r li

ne

grap

h:

�4

�3

�2

�1

01

23

4

Sol

ve 4

�2a

��

a.T

hen

grap

h i

t on

a n

um

ber

lin

e.

4 �

2a�

�a

Orig

inal

ineq

ualit

y

4 �

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2a�

�a

�2a

Add

2a

to e

ach

side

.

4 �

aS

impl

ify.

a�

44

�a

is t

he s

ame

as a

�4.

The

sol

utio

n in

set

-bui

lder

not

atio

n is

{a|

a�

4}.

Nu

mbe

r li

ne

grap

h:

�2

�1

01

23

45

6

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on,a

nd

gra

ph

it

on a

nu

mb

er l

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1.t

�12

�16

{tt

�28

}2.

n�

12 �

6{n

n�

18}

3.6

�g

�3

{gg

�9}

4.n

�8

��

13{n

n�

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5.�

12 �

�12

�y

{yy

�0}

6.�

6 �

s�

8{s

s�

2}

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

7.�

3x�

8 �

4x8.

0.6n

�12

�0.

4n9.

�8k

�12

��

9k{x

x�

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12}

{kk

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}

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y�

10 �

15 �

2y11

.z�

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4 �

3b

{yy

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}�z

z�

1�

{bb

��

4}

Def

ine

a va

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le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.13

–15.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

13.A

nu

mbe

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crea

sed

by 4

is

less

th

an 1

4.n

�4

�14

;{n

n�

18}

14.T

he

diff

eren

ce o

f tw

o n

um

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is

mor

e th

an 1

2,an

d on

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th

e n

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is

3.n

�3

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;{n

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15}

15.F

orty

is

no

grea

ter

than

th

e di

ffer

ence

of

a n

um

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and

2.40

�n

�2;

{nn

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}

2 � 34 � 31 � 3

�4

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01

23

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10

12

34

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�10

�8

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78

910

1112

1314

1514

1512

1316

1718

1920

2627

2829

3031

3233

34

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Solv

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by

Sub

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nS

ubtr

acti

on c

an b

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ed t

o so

lve

ineq

ualit

ies.

If a

nynu

mbe

r is

sub

trac

ted

from

eac

h si

de o

f a

true

ine

qual

ity,

the

resu

ltin

g in

equa

lity

is

also

tru

e.

Su

btr

acti

on

Pro

per

ty o

f In

equ

alit

ies

For

all

num

bers

a,

b, a

nd c

, if

a�

b, t

hen

a�

c�

b�

c,

and

if a

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n a

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e pr

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so t

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wh

en �

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a�

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5 �

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5 fr

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Sim

plify

.

Th

e so

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a�

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.N

um

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aph

:

Sol

ve e

ach

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hen

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eck

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ph

it

on a

nu

mb

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1.t

�12

�8

2.n

�12

��

123.

16 �

h�

9{t

t�

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{nn

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24}

{hh

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25.

3r�

6 �

4r6.

q�

5 �

q

{yy

��

6}{r

r�

6}{q

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5}

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ve e

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hen

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r so

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7.4p

�3p

�0.

78.

r�

�9.

9k�

12 �

8k

{pp

�0.

7}�r

r�

�{k

k�

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}

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1.2

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4 �

y11

.4y

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n�

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}{n

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ine

a va

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an

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olve

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en c

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k y

our

solu

tion

.13

–15.

Sam

ple

an

swer

:L

et n

�th

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um

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.

13.T

he

sum

of

a n

um

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and

8 is

les

s th

an 1

2.n

�8

�12

;{n

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4}

14.T

he

sum

of

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mos

t 6,

and

one

of t

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nu

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r is

�2.

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(�2)

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15.T

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num

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and

6 is

gre

ater

tha

n or

equ

al t

o �

4.n

�6

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4;{n

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�10

}

1 � 83 � 81 � 4

21

03

45

67

82

34

56

79

18

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�5

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0

1 � 23 � 2

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78

910

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13�

26�

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23�

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4�

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12

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Stu

dy G

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(c

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)

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lvin

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equ

alit

ies

by A

ddit

ion

an

d S

ub

trac

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-1

6-1

Exam

ple

Exam

ple

Exer

cises

Exer

cises

Answers (Lesson 6-1)


An

swer

s

Skil

ls P

ract

ice

So

lvin

g In

equ

alit

ies

by A

ddit

ion

an

d S

ub

trac

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

6-1

6-1

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lenc

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w-H

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5G

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Lesson 6-1

Mat

ch e

ach

in

equ

alit

y w

ith

its

cor

resp

ond

ing

grap

h.

1.x

�11

�16

ca.

2.x

�6

�1

eb

.

3.x

�2

��

3a

c.

4.x

�3

�1

bd

.

5.x

�1

��

7d

e.

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on,a

nd

gra

ph

it

on a

nu

mb

er l

ine.

6.d

�5

�1

{dd

�6}

7.s

�9

�8

{ss

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1}

8.a

�7

��

13{a

a�

�6}

9.w

�1

�4

{ww

�5}

10.4

�k

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{kk

�1}

11.�

9 �

b�

4{b

b�

�5}

12.�

2 �

x�

4{x

x�

�6}

13.2

y�

y�

2{y

y�

2}

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ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.14

–18.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

14.A

nu

mbe

r de

crea

sed

by 1

0 is

gre

ater

th

an �

5.n

�10

��

5;{n

n�

5}

15.A

nu

mbe

r in

crea

sed

by 1

is

less

th

an 9

.n

�1

�9;

{nn

�8}

16.S

even

mor

e th

an a

num

ber

is l

ess

than

or

equa

l to

�18

.n

�7

��

18;{

n n

��

25}

17.T

wen

ty l

ess

than

a n

um

ber

is a

t le

ast

15.

n�

20 �

15;

{nn

�35

}

18.A

nu

mbe

r pl

us

2 is

at

mos

t 1.

n�

2 �

1;{n

n�

�1}

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23

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lenc

oe A

lgeb

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Mat

ch e

ach

in

equ

alit

y w

ith

its

cor

resp

ond

ing

grap

h.

1.�

8 �

x�

15b

a.

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db

.

3.8x

�7x

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ac.

4.12

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cd

.

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on,a

nd

gra

ph

it

on a

nu

mb

er l

ine.

5.r

�(�

5) �

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��

7}6.

3x�

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4x{x

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ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.11

–14.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

11.T

he

sum

of

a n

um

ber

and

17 i

s n

o le

ss t

han

26.

n�

17 �

26;

{nn

�9}

12.T

wic

e a

nu

mbe

r m

inu

s 4

is l

ess

than

th

ree

tim

es t

he

nu

mbe

r.2n

�4

�3n

;{n

n�

�4}

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wel

ve i

s at

mos

t a

nu

mbe

r de

crea

sed

by 7

.12

�n

�7;

{nn

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}

14.E

igh

t pl

us

fou

r ti

mes

a n

um

ber

is g

reat

er t

han

fiv

e ti

mes

th

e n

um

ber.

8 �

4n�

5n;

{nn

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15.A

TMO

SPH

ERIC

SC

IEN

CE

Th

e tr

opos

pher

e ex

ten

ds f

rom

th

e ea

rth

’s s

urf

ace

to a

hei

ght

of 6

–12

mil

es,d

epen

din

g on

th

e lo

cati

on a

nd

the

seas

on.I

f a

plan

e is

fly

ing

at a

nal

titu

de o

f 5.

8 m

iles

,an

d th

e tr

opos

pher

e is

8.6

mil

es d

eep

in t

hat

are

a,h

ow m

uch

hig

her

can

th

e pl

ane

go w

ith

out

leav

ing

the

trop

osph

ere?

no

mo

re t

han

2.8

mi

16.E

AR

TH S

CIE

NC

EM

atu

re s

oil

is c

ompo

sed

of t

hre

e la

yers

,th

e u

pper

mos

t be

ing

tops

oil.

Jam

al i

s pl

anti

ng

a bu

sh t

hat

nee

ds a

hol

e 18

cen

tim

eter

s de

ep f

or t

he

root

s.T

he

inst

ruct

ion

s su

gges

t an

add

itio

nal

8 c

enti

met

ers

dept

h f

or a

cu

shio

n.I

f Ja

mal

wan

ts t

oad

d ev

en m

ore

cush

ion

,an

d th

e to

psoi

l in

his

yar

d is

30

cen

tim

eter

s de

ep,h

ow m

uch

mor

e cu

shio

n c

an h

e ad

d an

d st

ill

rem

ain

in

th

e to

psoi

l la

yer?

no

mo

re t

han

4 c

m

�4

�3

�2

�1

01

23

4�

4�

3�

2�

10

12

34

1 � 43 � 4

1 � 21 � 3

2 � 3

�4

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01

23

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10

12

34

45

23

67

89

10�

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7�

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10

23

45

67

81

0�8

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0

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6

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ctic

e (

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rag

e)

So

lvin

g In

equ

alit

ies

by A

ddit

ion

an

d S

ub

trac

tio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-1

6-1



Readin

g t

o L

earn

Math

em

ati

csS

olv

ing

Ineq

ual

itie

s by

Add

itio

n a

nd

Su

btr

acti

on

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-1

6-1

©G

lenc

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cGra

w-H

ill34

7G

lenc

oe A

lgeb

ra 1

Lesson 6-1

Pre-

Act

ivit

yH

ow a

re i

neq

ual

itie

s u

sed

to

des

crib

e sc

hoo

l sp

orts

?

Rea

d th

e in

trod

uct

ion

to

Les

son

6-1

at

the

top

of p

age

318

in y

our

text

book

.

•U

se t

he

info

rmat

ion

in

th

e gr

aph

to

wri

te a

n i

neq

ual

ity

stat

emen

t ab

out

part

icip

atio

n i

n t

wo

spor

ts.

Sam

ple

an

swer

:F

or

soft

bal

l an

d t

rack

an

d f

ield

,13,

009

�14

,587

•R

ewri

te y

our

ineq

ual

ity

stat

emen

t to

sh

ow t

hat

40

sch

ools

add

ed b

oth

of

the

spor

ts.I

s th

e st

atem

ent

stil

l tr

ue?

Sam

ple

an

swer

:13

,049

�14

,627

;ye

s

Rea

din

g t

he

Less

on

Wri

te t

he

lett

er o

f th

e gr

aph

th

at m

atch

es e

ach

in

equ

alit

y.

1.x

��

1a.

2.x

��

1b

.

3.x

��

1c.

4.x

��

1d

.

5.U

se t

he

char

t to

wri

te a

sen

ten

ce t

hat

cou

ld b

e de

scri

bed

by t

he

ineq

ual

ity

3n�

2n�

7.T

hen

sol

ve t

he

ineq

ual

ity.

Ineq

ual

itie

s

��

��

less

tha

ngr

eate

r th

anat

mos

tat

leas

tfe

wer

tha

nm

ore

than

no m

ore

than

no le

ss t

han

less

tha

n or

equ

al t

ogr

eate

r th

an o

r eq

ual t

o

Sam

ple

an

swer

:Th

ree

tim

es a

nu

mb

er is

at

leas

t tw

o t

imes

th

e n

um

ber

plu

s 7;

n�

7

Hel

pin

g Y

ou

Rem

emb

er

6.T

each

ing

som

eon

e el

se c

an h

elp

you

rem

embe

r so

met

hin

g.E

xpla

in h

ow y

ou w

ould

tea

chan

oth

er s

tude

nt

wh

o m

isse

d cl

ass

to s

olve

th

e in

equ

alit

y 2x

�4

�3x

.

Su

btr

act

2xfr

om

eac

h s

ide.

Sim

plif

y.

32

10

�1

�2

�3

c3

21

0�

1�

2�

3a

�3

�2

�1

01

23

d�

3�

2�

10

12

3b

©G

lenc

oe/M

cGra

w-H

ill34

8G

lenc

oe A

lgeb

ra 1

Tria

ng

le In

equ

alit

ies

Rec

all

that

a l

ine

segm

ent

can

be

nam

ed b

y th

e le

tter

s of

its

en

dpoi

nts

.Lin

e se

gmen

t A

B(w

ritt

en a

s A �

B�)

has

poi

nts

Aan

d B

for

endp

oin

ts.T

he

len

gth

of A

Bis

wri

tten

wit

hou

t th

e ba

r as

AB

.

AB

�B

Cm

�A

�m

�B

Th

e st

atem

ent

on t

he

left

abo

ve s

how

s th

at A �

B�is

sh

orte

r th

an B�

C�.

Th

e st

atem

ent

on t

he

righ

t ab

ove

show

s th

at t

he

mea

sure

of

angl

e A

is l

ess

than

th

at o

f an

gle

B.

Th

ese

thre

e in

equ

alit

ies

are

tru

e fo

r an

y tr

ian

gle

AB

C,

no

mat

ter

how

lon

g th

e si

des.

a.A

B�

BC

�A

Cb

.If

AB

�A

C,t

hen

m�

C�

m�

B.

c.If

m�

C�

m�

B,t

hen

AB

�A

C.

Use

th

e th

ree

tria

ngl

e in

equ

alit

ies

for

thes

e p

rob

lem

s.

1.L

ist

the

side

s of

tri

angl

e D

EF

in o

rder

of

incr

easi

ng

len

gth

.

D�F�,

D�E�

,E�F�

2.In

th

e fi

gure

at

the

righ

t,w

hic

h l

ine

segm

ent

is t

he

shor

test

?

L�M�

3.E

xpla

in w

hy

the

len

gth

s 5

cm,1

0 cm

,an

d 20

cm

cou

ld n

ot b

e u

sed

to m

ake

a tr

ian

gle.

5 �

10 is

no

t g

reat

er t

han

20.

4.T

wo

side

s of

a t

rian

gle

mea

sure

3 i

n.a

nd

7 in

.Bet

wee

n w

hic

h t

wo

valu

es m

ust

th

e th

ird

side

be?

4 in

.an

d 1

0 in

.

5.In

tri

angl

e X

YZ

,XY

�15

,YZ

�12

,an

d X

Z�

9.W

hic

h i

s th

egr

eate

st a

ngl

e? W

hic

h i

s th

e le

ast?

�Z

;�

Y

6.L

ist

the

angl

es �

A,�

C,�

AB

C,a

nd

�A

BD

,in

ord

er o

f in

crea

sin

g si

ze.

�A

BD

,�A

,�A

BC

,�C

C ADB

13 1512

5 9

JM

K

L

65

60

65

55

65

50

D

FE

60

35

85

A

BC

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-1

6-1



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

So

lvin

g In

equ

alit

ies

by M

ult

iplic

atio

n a

nd

Div

isio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-2

6-2

©G

lenc

oe/M

cGra

w-H

ill34

9G

lenc

oe A

lgeb

ra 1

Lesson 6-2

Solv

e In

equ

alit

ies

by

Mu

ltip

licat

ion

If e

ach

sid

e of

an

in

equ

alit

y is

mu

ltip

lied

by

the

sam

e po

siti

ve n

um

ber,

the

resu

ltin

g in

equ

alit

y is

als

o tr

ue.

How

ever

,if

each

sid

e of

an

ineq

ual

ity

is m

ult

ipli

ed b

y th

e sa

me

neg

ativ

e n

um

ber,

the

dire

ctio

n o

f th

e in

equ

alit

y m

ust

be r

ever

sed

for

the

resu

ltin

g in

equ

alit

y to

be

tru

e.

For

all

num

bers

a,

b, a

nd c

, w

ith c

0,

1.if

cis

pos

itive

and

a�

b, t

hen

ac�

bc;

Mu

ltip

licat

ion

Pro

per

ty o

f In

equ

alit

ies

if c

is p

ositi

ve a

nd a

�b,

the

n ac

�bc

;

2.if

cis

neg

ativ

e an

d a

�b,

the

n ac

�bc

;if

cis

neg

ativ

e an

d a

�b,

the

n ac

�bc

.

Th

e pr

oper

ty i

s al

so t

rue

wh

en �

and

�ar

e re

plac

ed w

ith

�an

d �

.

Sol

ve �

�12

.

��

12O

rigin

al e

quat

ion

(�8)��

��(�

8)12

Mul

tiply

eac

h si

de b

y �

8; c

hang

e �

to �

.

y�

�96

Sim

plify

.

Th

e so

luti

on i

s {y

y�

�96

}.

y � 8y � 8

y � 8S

olve

k

�15

.

k�

15O

rigin

al e

quat

ion

��k

��

15M

ultip

ly e

ach

side

by

.

k�

20S

impl

ify.

Th

e so

luti

on i

s {k

k�

20}.

4 � 34 � 3

3 � 44 � 3

3 � 4

3 � 4Ex

ampl

e1Ex

ampl

e1Ex

ampl

e2Ex

ampl

e2

Exer

cises

Exer

cises

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

1.�

22.

��

223.

h�

�3

4.�

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6

{yy

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00}

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b�

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b�

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412

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{gg

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�p p

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{nn

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}{a

a�

�21

}

Def

ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.13

–15.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

13.H

alf

of a

nu

mbe

r is

at

leas

t 14

.n

�14

;{n

n�

28}

14.T

he

oppo

site

of

one-

thir

d a

nu

mbe

r is

gre

ater

th

an 9

.�

n�

9;{n

n�

�27

}

15.O

ne

fift

h o

f a

nu

mbe

r is

at

mos

t 30

.n

�30

;{n

n�

150}

1 � 5

1 � 3

1 � 25 � 12

2a � 7n � 10

9p � 53 � 4

g � 5

1 � 41 � 2

2h � 43 � 20

3m �5

1 � 32 � 3

1 � 4

p � 63 � 5

n � 50y � 6

©G

lenc

oe/M

cGra

w-H

ill35

0G

lenc

oe A

lgeb

ra 1

Solv

e In

equ

alit

ies

by

Div

isio

nIf

eac

h s

ide

of a

tru

e in

equ

alit

y is

div

ided

by

the

sam

e po

siti

ve n

um

ber,

the

resu

ltin

g in

equ

alit

y is

als

o tr

ue.

How

ever

,if

each

sid

e of

an

ineq

ual

ity

is d

ivid

ed b

y th

e sa

me

neg

ativ

e n

um

ber,

the

dire

ctio

n o

f th

e in

equ

alit

y sy

mbo

lm

ust

be

reve

rsed

for

th

e re

sult

ing

ineq

ual

ity

to b

e tr

ue.

For

all

num

bers

a,

b, a

nd c

with

c

0,

Div

isio

n P

rop

erty

1.if

cis

pos

itive

and

a�

b, t

hen

�;

if c

is p

ositi

ve a

nd a

�b,

the

n �

;o

f In

equ

alit

ies

2.if

cis

neg

ativ

e an

d a

�b,

the

n �

; if

cis

neg

ativ

e an

d a

�b,

the

n �

.

Th

e pr

oper

ty i

s al

so t

rue

wh

en �

and

�ar

e re

plac

ed w

ith

�an

d �

.

Sol

ve �

12y

�48

.

�12

y�

48O

rigin

al in

equa

lity

�D

ivid

e ea

ch s

ide

by �

12 a

nd c

hang

e �

to �

.

y�

�4

Sim

plify

.

Th

e so

luti

on i

s {y

y�

�4}

.

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

1.25

g�

�10

02.

�2x

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3.�

5c�

24.

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6k�

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0.24

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_

6-3

6-3

©G

lenc

oe/M

cGra

w-H

ill35

5G

lenc

oe A

lgeb

ra 1

Lesson 6-3

Solv

e M

ult

i-St

ep In

equ

alit

ies

To

solv

e li

nea

r in

equ

alit

ies

invo

lvin

g m

ore

than

on

eop

erat

ion

,un

do t

he

oper

atio

ns

in r

ever

se o

f th

e or

der

of o

pera

tion

s,ju

st a

s yo

u w

ould

sol

vean

equ

atio

n w

ith

mor

e th

an o

ne

oper

atio

n.

Sol

ve 6

x�

4 �

2x�

12.

6x�

4 �

2x�

12O

rigin

al in

equa

lity

6x�

4 �

2x�

2x�

12 �

2xS

ubtr

act

2xfr

om

each

sid

e.

4x�

4 �

12S

impl

ify.

4x�

4 �

4 �

12 �

4A

dd 4

to

each

sid

e.

4x�

16S

impl

ify.

�D

ivid

e ea

ch s

ide

by 4

.

x�

4S

impl

ify.

Th

e so

luti

on i

s {x

x�

4}.

16 � 44x � 4

Sol

ve 3

a�

15 �

4 �

5a.

3a�

15 �

4 �

5aO

rigin

al in

equa

lity

3a�

15 �

5a�

4 �

5a�

5aS

ubtr

act

5afr

om

each

sid

e.

�2a

�15

�4

Sim

plify

.

�2a

�15

�15

�4

�15

Add

15

to e

ach

side

.

�2a

�19

Sim

plify

.

�D

ivid

e ea

ch s

ide

by �

2

and

chan

ge �

to �

.

a�

�9

Sim

plify

.

Th

e so

luti

on i

s �a

a�

�9

�.1 � 2

1 � 2

19 � �2

�2a

� �2

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

1.11

y�

13 �

�1

2.8n

�10

�6

�2n

3.�

1 �

�5

�y y

��

1�

�n n

�1

�{q

q�

�42

}

4.6n

�12

�8

�8n

5.�

12 �

d�

�12

�4d

6.5r

�6

�8r

�18

{nn

�2}

{dd

�0}

{rr

�4}

7.�

128.

7.3y

�14

.4 �

4.9y

9.�

8m�

3 �

18 �

m

{xx

��

6}{y

y�

6}{m

m�

�3}

10.�

4y�

10 �

19 �

2y11

.9n

�24

n�

45 �

012

.�

�4

�y y

��

14�

{nn

�3}

�x x

��

4�

Def

ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.13

–15.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

13.N

egat

ive

thre

e ti

mes

a n

um

ber

plu

s fo

ur

is n

o m

ore

than

th

e n

um

ber

min

us

eigh

t.�

3n�

4 �

n�

8;{n

n�

3}

14.O

ne

fou

rth

of

a n

um

ber

decr

ease

d by

th

ree

is a

t le

ast

two.

n�

3 �

2;{n

n�

20}

15.T

he

sum

of

twel

ve a

nd

a n

um

ber

is n

o gr

eate

r th

an t

he

sum

of

twic

e th

e n

um

ber

and

�8.

12 �

n�

2n�

(�8)

;{n

n�

20}

1 � 4

1 � 21 � 2

4x�

2�

5

�3x

�6

�� 2

3 � 53 � 11

q � 7

©G

lenc

oe/M

cGra

w-H

ill35

6G

lenc

oe A

lgeb

ra 1

Solv

e In

equ

alit

ies

Invo

lvin

g t

he

Dis

trib

uti

ve P

rop

erty

Wh

en s

olvi

ng

ineq

ual

itie

s th

at c

onta

in g

rou

pin

g sy

mbo

ls,f

irst

use

th

e D

istr

ibu

tive

Pro

pert

y to

rem

ove

the

grou

pin

g sy

mbo

ls.T

hen

un

do t

he

oper

atio

ns

in r

ever

se o

f th

e or

der

of o

pera

tion

s,ju

st a

s yo

uw

ould

sol

ve a

n e

quat

ion

wit

h m

ore

than

on

e op

erat

ion

.

Sol

ve 3

a�

2(6a

�4)

�4

�(4

a�

6).

3a�

2(6a

�4)

�4

�(4

a�

6)O

rigin

al in

equa

lity

3a�

12a

�8

�4

�4a

�6

Dis

trib

utiv

e P

rope

rty

�9a

�8

��

2 �

4aC

ombi

ne li

ke t

erm

s.

�9a

�8

�4a

��

2 �

4a�

4aA

dd 4

ato

eac

h si

de.

�5a

�8

��

2C

ombi

ne li

ke t

erm

s.

�5a

�8

�8

��

2 �

8S

ubtr

act

8 fr

om e

ach

side

.

�5a

��

10S

impl

ify.

a�

2D

ivid

e ea

ch s

ide

by �

5 an

d ch

ange

�to

�.

Th

e so

luti

on i

n s

et-b

uil

der

not

atio

n i

s {a

a�

2}.

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

1.2(

t�

3) �

162.

3(d

�2)

�2d

�16

3.4h

�8

�2(

h�

1)

{tt

�5}

{dd

�22

}{h

h�

3}

4.6y

�10

�8

�(y

�14

)5.

4.6(

x�

3.4)

�5.

1x6.

�5x

�(2

x�

3) �

1

�y y

��

2�

{xx

��

31.2

8}�x

x�

��

7.3(

2y�

4) �

2(y

�1)

�10

8.8

�2(

b�

1) �

12 �

3b9.

�2(

k�

1) �

8(1�

k)

{yy

�6}

{bb

�6}

�k k

��

�10

.0.3

(y�

2) �

0.4(

1 �

y)11

.m�

17 �

�(4

m�

13)

{yy

��

10}

�mm

��

�12

.3n

�8

�2(

n�

4) �

2(1

�n

)13

.2(y

�2)

��

4 �

2y

{nn

�18

}�

14.k

�17

��

(17

�k)

15.n

�4

��

3(2

�n

)

{kk

is a

rea

l nu

mb

er}

�n n

��

�D

efin

e a

vari

able

,wri

te a

n i

neq

ual

ity,

and

sol

ve e

ach

pro

ble

m.T

hen

ch

eck

you

rso

luti

on.

16–1

8.S

amp

le a

nsw

er:

Let

n�

the

nu

mb

er.

16.T

wic

e th

e su

m o

f a

nu

mbe

r an

d 4

is l

ess

than

12.

2(n

�4)

�12

;{n

n�

2}

17.T

hre

e ti

mes

th

e su

m o

f a

nu

mbe

r an

d si

x is

gre

ater

th

an f

our

tim

es t

he

nu

mbe

rde

crea

sed

by t

wo.

3(n

�6)

�4n

�2;

{nn

�20

}

18.T

wic

e th

e di

ffer

ence

of

a n

um

ber

and

fou

r is

les

s th

an t

he

sum

of

the

nu

mbe

r an

d fi

ve.

2(n

�4)

�n

�5;

{nn

�13

}

1 � 2

4 � 5

3 � 54 � 72 � 7

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

So

lvin

g M

ult

i-S

tep

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Skil

ls P

ract

ice

So

lvin

g M

ult

i-S

tep

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3

©G

lenc

oe/M

cGra

w-H

ill35

7G

lenc

oe A

lgeb

ra 1

Lesson 6-3

Ju

stif

y ea

ch i

nd

icat

ed s

tep

.

1.t

�3

��

15

t�

3 �

3 �

�15

�3

a.

t�

�12

��t�

(�12

)b

.

t�

�16

a.A

dd

3 t

o e

ach

sid

e.b

.Mu

ltip

ly e

ach

sid

e by

.

2.5(

k�

8) �

7 �

235k

�40

�7

�23

a.5k

�33

�23

5k�

33 �

33 �

23 �

33b

.5k

��

10

�c.

k�

�2

a.D

istr

ibu

tive

Pro

per

tyb

.Su

btr

act

33 f

rom

eac

h s

ide.

c.D

ivid

e ea

ch s

ide

by 5

.

?�

10�

55k � 5

??

4 � 3

?4 � 3

3 � 44 � 3

3 � 4

?3 � 4

3 � 4

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

3.�

2b�

4 �

�6

4.3x

�15

�21

5.�

1 �

3

{bb

�5}

{xx

�2}

{dd

�8}

6.a

�4

�2

7.�

�7

��

48.

j�

10 �

5

{aa

�15

}{t

t�

55}

{jj

�20

}

9.�

f�

3 �

�9

10.2

p�

5 �

3p�

1011

.4k

�15

��

2k�

3

{ff

�18

}{p

p�

15}

{kk

��

2}

12.2

(�3m

�5)

��

2813

.�6(

w�

1) �

2(w

�5)

14.2

(q�

3) �

6 �

�10

{mm

�3}

{ww

��

2}{q

q�

�5}

Def

ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.15

–20.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

15.F

our

mor

e th

an t

he

quot

ien

t of

a n

um

ber

and

thre

e is

at

leas

t n

ine.

�4

�9;

{ nn

�15

}

16.T

he

sum

of

a n

um

ber

and

fou

rtee

n i

s le

ss t

han

or

equ

al t

o th

ree

tim

es t

he

nu

mbe

r.n

�14

�3n

;{n

n�

7}

17.N

egat

ive

thre

e ti

mes

a n

um

ber

incr

ease

d by

sev

en i

s le

ss t

han

neg

ativ

e el

even

.�

3n�

7 �

�11

;{n

n�

6}

18.F

ive

tim

es a

nu

mbe

r de

crea

sed

by e

igh

t is

at

mos

t te

n m

ore

than

tw

ice

the

nu

mbe

r.5n

�8

�2n

�10

;{n

n�

6}

19.S

even

mor

e th

an f

ive

sixt

hs

of a

nu

mbe

r is

mor

e th

an n

egat

ive

thre

e.n

�7

��

3;{ n

n�

�12

}

20.F

our

tim

es t

he

sum

of

a n

um

ber

and

two

incr

ease

d by

th

ree

is a

t le

ast

twen

ty-s

even

.4(

n�

2) �

3 �

27;

{nn

�4}

5 � 6

n � 3

2 � 3

3 � 4t � 5

2 � 5

d � 2

©G

lenc

oe/M

cGra

w-H

ill35

8G

lenc

oe A

lgeb

ra 1

Ju

stif

y ea

ch i

nd

icat

ed s

tep

.

Pra

ctic

e (

Ave

rag

e)

So

lvin

g M

ult

i-S

tep

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3

1.x

�

8x�

(8)

a.

8x�

5x�

128x

�5x

�5x

�12

�5x

b.

3x�

�12

�c.

x�

�4

a.M

ult

iply

eac

h s

ide

by 8

.b

.Su

btr

act

5 xfr

om

eac

h s

ide.

c.D

ivid

e ea

ch s

ide

by 3

.

2.2(

2h�

2) �

2(3h

�5)

�12

4h�

4 �

6h�

10 �

12a.

4h�

4 �

6h�

24h

�4

�6h

�6h

�2

�6h

b.

�2h

�4

��

2�

2h�

4 �

4 �

�2

�4

c.�

2h�

�6

�d

.

h�

3a.

Dis

trib

uti

ve P

rop

erty

b.S

ub

trac

t 6 h

fro

m e

ach

sid

e.c.

Su

btr

act

4 fr

om

eac

h s

ide.

d.D

ivid

e ea

ch s

ide

by �

2 an

dch

ang

e �

to �

.

?�

6� �

2�

2h� �

2

???

?�

12�

33x � 3

??5x

�12

�8

5x�

12�

8

Sol

ve e

ach

in

equ

alit

y.T

hen

ch

eck

you

r so

luti

on.

3.�

5 �

��

94.

4u�

6 �

6u�

205.

13 �

a�

1

{tt

�24

}{u

u�

7}{a

a�

21}

6.�

�8

{ww

��

19}

7.�

7{f

f�

15}

8.h

�{h

h�

�3}

9.3(

z�

1) �

11 �

�2(

z�

13)

{zz

��

8}

10.3

e�

2(4e

�2)

�2(

6e�

1){e

e�

2}11

.5n

�3(

n�

6) �

0{n

n�

�9}

Def

ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.12

–13.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

12.A

nu

mbe

r is

les

s th

an o

ne

fou

rth

th

e su

m o

f th

ree

tim

es t

he

nu

mbe

r an

d fo

ur.

n�

;{n

n�

4}13

.Tw

o ti

mes

th

e su

m o

f a

nu

mbe

r an

d fo

ur

is n

o m

ore

than

th

ree

tim

es t

he

sum

of

the

nu

mbe

r an

d se

ven

dec

reas

ed b

y fo

ur.

2(n

�4)

�3(

n�

7) �

4;{n

n�

�9}

14.G

EOM

ETRY

Th

e ar

ea o

f a

tria

ngu

lar

gard

en c

an b

e n

o m

ore

than

120

squ

are

feet

.Th

eba

se o

f th

e tr

ian

gle

is 1

6 fe

et.W

hat

is

the

hei

ght

of t

he

tria

ngl

e?n

o m

ore

th

an 1

5 ft

15.M

USI

C P

RA

CTI

CE

Nab

uko

pra

ctic

es t

he

viol

in a

t le

ast

12 h

ours

per

wee

k.S

he

prac

tice

s fo

r th

ree

fou

rth

s of

an

hou

r ea

ch s

essi

on.I

f N

abu

ko h

as a

lrea

dy p

ract

iced

3

hou

rs i

n o

ne

wee

k,h

ow m

any

sess

ion

s re

mai

n t

o m

eet

or e

xcee

d h

er w

eekl

y pr

acti

ce g

oal?

at le

ast

12 s

essi

on

s

3n�

4�

4

6h�

3�

5

3f�

10�

5w

�3

�2

2 � 3t � 6



Readin

g t

o L

earn

Math

em

ati

csS

olv

ing

Mu

lti-

Ste

p In

equ

alit

ies

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3

©G

lenc

oe/M

cGra

w-H

ill35

9G

lenc

oe A

lgeb

ra 1

Lesson 6-3

Pre-

Act

ivit

yH

ow a

re l

inea

r in

equ

alit

ies

use

d i

n s

cien

ce?

Rea

d th

e in

trod

uct

ion

to

Les

son

6-3

at

the

top

of p

age

332

in y

our

text

book

.T

hen

wri

te a

n i

neq

ual

ity

that

cou

ld b

e u

sed

to f

ind

the

tem

pera

ture

s in

degr

ees

Cel

siu

s fo

r w

hic

h e

ach

su

bsta

nce

is

a ga

s.

Arg

on:

C�

32 �

�30

3B

rom

ine:

C�

32 �

138

Rea

din

g t

he

Less

on

1.W

hat

does

the

phr

ase

“und

oing

the

ope

rati

ons

in r

ever

se o

f th

e or

der

of o

pera

tion

s”m

ean?

Sam

ple

an

swer

:F

irst

ad

d o

r su

btr

act

to u

nd

o s

ub

trac

tio

n o

r ad

dit

ion

,th

en m

ult

iply

or

div

ide

to u

nd

o d

ivis

ion

or

mu

ltip

licat

ion

.

2.D

escr

ibe

how

ch

ecki

ng

the

solu

tion

of

an i

neq

ual

ity

is d

iffe

ren

t fr

om c

hec

kin

g th

eso

luti

on o

f an

equ

atio

n.

Sam

ple

an

swer

:In

stea

d o

f su

bst

itu

tin

g o

ne

valu

e fo

r th

e va

riab

le,t

her

ear

e in

fin

itel

y m

any

valu

es t

hat

can

be

use

d t

o c

hec

k.It

is a

go

od

idea

to

use

a v

alu

e th

at is

less

th

an,t

he

valu

e eq

ual

to

,an

d a

val

ue

gre

ater

th

anth

e n

um

ber

in t

he

solu

tio

n t

o c

hec

k an

ineq

ual

ity.

3.D

escr

ibe

how

th

e D

istr

ibu

tive

Pro

pert

y ca

n b

e u

sed

to r

emov

e th

e gr

oupi

ng

sym

bols

in

the

ineq

ual

ity

4x�

7(2x

�8)

�3x

�5.

Mu

ltip

ly �

7 by

bo

th 2

xan

d 8

.

4.Is

it

poss

ible

to

hav

e n

o so

luti

on w

hen

you

sol

ve a

n i

neq

ual

ity?

Exp

lain

you

r an

swer

an

dgi

ve a

n e

xam

ple.

Sam

ple

an

swer

:Yes

;if

so

lvin

g r

esu

lts

in a

n in

equ

alit

y th

at is

nev

er t

rue

(an

d t

he

sig

ns

hav

e b

een

rev

erse

d if

nec

essa

ry),

then

th

ere

is n

oso

luti

on

.Exa

mp

le:

3(t

�4)

�8

�3

(t�

4) �

8

Hel

pin

g Y

ou

Rem

emb

er

5.M

ake

a ch

eckl

ist

of s

teps

you

can

use

wh

en s

olvi

ng

ineq

ual

itie

s.

(1)

Use

th

e D

istr

ibu

tive

Pro

per

ty t

o r

emov

e an

y g

rou

pin

g s

ymb

ols

.(2

)C

om

bin

e an

y lik

e te

rms.

(3)

Ad

d o

r su

btr

act

the

sam

e va

riab

le t

erm

s o

r co

nst

ants

on

bo

th s

ides

.(4

)M

ult

iply

or

div

ide

to u

nd

o o

per

atio

ns.

(5)

Rev

erse

th

e d

irec

tio

n o

f th

e in

equ

alit

y sy

mb

ol i

f b

oth

sid

es w

ere

mu

ltip

lied

or

div

ided

by

a n

egat

ive

nu

mb

er.

(6)

Be

sure

th

e va

riab

le is

by

itse

lf o

n o

ne

sid

e o

f th

e fi

nal

ineq

ual

ity.

9 � 59 � 5

©G

lenc

oe/M

cGra

w-H

ill36

0G

lenc

oe A

lgeb

ra 1

Car

los

Mo

nte

zum

a D

uri

ng

his

lif

etim

e,C

arlo

s M

onte

zum

a (1

865?

–192

3) w

as o

ne

of t

he

mos

t in

flu

enti

al N

ativ

e A

mer

ican

s in

th

e U

nit

ed S

tate

s.H

e w

asre

cogn

ized

as

a pr

omin

ent

phys

icia

n a

nd

was

als

o a

pass

ion

ate

advo

cate

of t

he

righ

ts o

f N

ativ

e A

mer

ican

peo

ples

.Th

e ex

erci

ses

that

fol

low

wil

lh

elp

you

lea

rn s

ome

inte

rest

ing

fact

s ab

out

Dr.

Mon

tezu

ma’

s li

fe.

Sol

ve e

ach

in

equ

alit

y.T

he

wor

d o

r p

hra

se n

ext

to t

he

equ

ival

ent

ineq

ual

ity

wil

l co

mp

lete

th

e st

atem

ent

corr

ectl

y.

1.�

2k�

102.

5 �

r�

9 M

onte

zum

a w

as b

orn

in

th

e st

ate

He

was

a N

ativ

e A

mer

ican

of

the

of

.Ya

vapa

is,w

ho

are

a pe

ople

.

a.k

��

5A

rizo

na

a.r

��

4N

avaj

o

b.

k�

�5

Mon

tan

ab

.r

��

4M

ohaw

k

c.k

�12

Uta

hc.

r�

14M

ohav

e-A

pach

e

3.�

y�

�9

4.�

3 �

q�

12

Mon

tezu

ma

rece

ived

a m

edic

alA

s a

phys

icia

n,M

onte

zum

a's

fiel

d of

de

gree

fro

m

in 1

889.

spec

iali

zati

on w

as

.

a.y

�9

Ch

icag

o M

edic

al C

olle

gea.

q�

�4

hea

rt s

urg

ery

b.

y�

�9

Har

vard

Med

ical

Sch

ool

b.

q�

15in

tern

al m

edic

ine

c.y

�9

Joh

ns

Hop

kin

s U

niv

ersi

tyc.

q�

�15

resp

irat

ory

dise

ases

5.5

�4x

�14

�x

6.7

�t

�7

�t

For

mu

ch o

f h

is c

aree

r,h

e m

ain

tain

ed

In a

ddit

ion

to

mai

nta

inin

g h

is m

edic

ala

med

ical

pra

ctic

e in

.

prac

tice

,he

was

als

o a(

n)

.

a.x

�9

New

Yor

k C

ity

a.t

�7

dire

ctor

of

a bl

ood

ban

k

b.

x�

3C

hic

ago

b.

t�

0in

stru

ctor

at

a m

edic

al c

olle

ge

c.x

��

9B

osto

nc.

t�

�7

lega

l co

un

sel

to p

hys

icia

ns

7.3a

�8

�4a

�10

8.6n

�8n

�12

M

onte

zum

a fo

un

ded,

wro

te,a

nd

Mon

tezu

ma

test

ifie

d be

fore

a

edit

ed

,a m

onth

ly n

ewsl

ette

rco

mm

itte

e of

th

e U

nit

ed S

tate

s th

at a

ddre

ssed

Nat

ive

Am

eric

anC

ongr

ess

con

cern

ing

his

wor

k in

co

nce

rns.

trea

tin

g .

a.a

��

2Ya

vapa

ia.

n�

6ap

pen

dici

tis

b.

a�

18A

pach

eb

.n

��

6as

thm

a

c.a

�18

Was

saja

c.n

��

10h

eart

att

acks

?

?

??

??

??

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

So

lvin

g C

om

po

un

d In

equ

alit

ies

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4

©G

lenc

oe/M

cGra

w-H

ill36

1G

lenc

oe A

lgeb

ra 1

Lesson 6-4

Ineq

ual

itie

s C

on

tain

ing

an

dA

com

pou

nd

ineq

ual

ity

con

tain

ing

and

is t

rue

only

if

both

in

equ

alit

ies

are

tru

e.T

he

grap

h o

f a

com

pou

nd

ineq

ual

ity

con

tain

ing

and

is t

he

inte

rsec

tion

of t

he

grap

hs

of t

he

two

ineq

ual

itie

s.E

very

sol

uti

on o

f th

e co

mpo

un

din

equ

alit

y m

ust

be

a so

luti

on o

f bo

th i

neq

ual

itie

s.

Gra

ph

th

e so

luti

onse

t of

x�

2 an

d x

��

1. Gra

ph x

�2.

Gra

ph x

��

1.

Fin

d th

e in

ters

ectio

n.

Th

e so

luti

on s

et i

s {x

�1

�x

�2}

.

�2

�1

�3

01

23

�3

�2

�1

01

23

�3

�2

�1

01

23

Sol

ve �

1 �

x�

2 �

3 u

sin

ga

nd

.Th

en g

rap

h t

he

solu

tion

set

.

�1

�x

�2

and

x�

2 �

3�

1 �

2 �

x�

2 �

2x

�2

�2

�3

�2

�3

�x

x�

1

Gra

ph x

��

3.

Gra

ph x

�1.

Fin

d th

e in

ters

ectio

n.

Th

e so

luti

on s

et i

s {x

�3

�x

�1}

.

�2

�1

�4

�3

01

2

�3

�4

�2

�1

01

2

�3

�4

�2

�1

01

2

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Gra

ph

th

e so

luti

on s

et o

f ea

ch c

omp

oun

d i

neq

ual

ity.

1.b

��

1 an

d b

�3

2.2

�q

��

53.

x�

�3

and

x�

4

4.�

2 �

p�

45.

�3

�d

and

d�

26.

�1

�p

�3

Sol

ve e

ach

com

pou

nd

in

equ

alit

y.T

hen

gra

ph

th

e so

luti

on s

et.

7.4

�w

�3

�5

8.�

3 �

p�

5 �

2{w

1 �

w�

2}{p

2 �

p�

7}

9.�

4 �

x�

2 �

�2

10.y

�1�

2 an

d y

�2

�1

{x�

6 �

x�

�4}

{y�

1 �

y�

3}

11.n

�2

��

3 an

d n

�4

�6

12.d

�3

�6d

�12

�2d

�32

{n�

1 �

n�

2}{d

�3

�d

�5}

�3

�2

�1

01

23

45

�3

�4

�2

�1

01

23

4

�3

�4

�2

�1

01

23

4�

7�

6�

5�

4�

3�

2�

10

1

01

23

45

67

8�

3�

4�

2�

10

12

34

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�4

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�1

01

23

4�

3�

4�

2�

10

12

34

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�1

01

23

45

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�3

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01

23

4�

4�

3�

6�

5�

2�

10

12

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�3

�2

�1

01

23

4

©G

lenc

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cGra

w-H

ill36

2G

lenc

oe A

lgeb

ra 1

Ineq

ual

itie

s C

on

tain

ing

or

A c

ompo

un

d in

equ

alit

y co

nta

inin

g or

is t

rue

if o

ne

orbo

th o

f th

e in

equ

alit

ies

are

tru

e.T

he

grap

h o

f a

com

pou

nd

ineq

ual

ity

con

tain

ing

oris

th

eu

nio

nof

th

e gr

aph

s of

th

e tw

o in

equ

alit

ies.

Th

e u

nio

n c

an b

e fo

un

d by

gra

phin

g bo

thin

equ

alit

ies

on t

he

sam

e n

um

ber

lin

e.A

sol

uti

on o

f th

e co

mpo

un

d in

equ

alit

y is

a s

olu

tion

of

eith

er i

neq

ual

ity,

not

nec

essa

rily

bot

h.

Sol

ve 2

a�

1 �

11 o

r a

�3a

�2.

2a�

1 �

11or

a�

3a�

22a

�1

�1

�11

�1

a�

3a�

3a�

3a�

22a

�10

�2a

�2

��

a�

5a

��

1

Gra

ph a

�5.

Gra

ph a

��

1.

Fin

d th

e un

ion.

Th

e so

luti

on s

et i

s {a

a�

5}.

Gra

ph

th

e so

luti

on s

et o

f ea

ch c

omp

oun

d i

neq

ual

ity.

1.b

�2

or b

��

32.

3 �

qor

q�

13.

y�

�4

or y

�0

4.4

�p

or p

�8

5.�

3 �

dor

d�

26.

�2

�x

or 3

�x

Sol

ve e

ach

com

pou

nd

in

equ

alit

y.T

hen

gra

ph

th

e so

luti

on s

et.

7.3

�3w

or 3

w�

98.

�3p

�1

��

11 o

r p

�2

{w1

�w

}{p

p�

4 o

r p

�2}

9.2x

�4

�6

or x

�2x

�4

10.2

y�

2 �

12 o

r y

�3

�2y

{xx

�4}

{yy

�5}

11.

n�

�2

or 2

n�

2 �

6 �

n12

.3a

�2

�5

or 7

�3a

�2a

�6

{nn

is a

rea

l nu

mb

er}

{aa

��

1 o

r a

�1}

0�

1�

2�

3�

41

23

40

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12

34

1 � 2

01

23

45

67

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10

12

34

56

01

23

45

67

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3�

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2�

10

12

34

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01

23

40

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12

34

0�

1�

21

23

45

6

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01

23

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01

23

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10

12

34

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01

23

45

6

�2

�1

01

23

45

6

�2

�1

01

23

45

6

2� �

2�

2a� �

210 � 2

2a � 2

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

So

lvin

g C

om

po

un

d In

equ

alit

ies

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

So

lvin

g C

om

po

un

d In

equ

alit

ies

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4

©G

lenc

oe/M

cGra

w-H

ill36

3G

lenc

oe A

lgeb

ra 1

Lesson 6-4

Gra

ph

th

e so

luti

on s

et o

f ea

ch c

omp

oun

d i

neq

ual

ity.

1.b

�3

or b

�0

2.z

�3

and

z�

�2

3.k

�1

and

k�

54.

y�

�1

or y

�1

Wri

te a

com

pou

nd

in

equ

alit

y fo

r ea

ch g

rap

h.

5.6.

�3

�x

�3

1 �

x�

4

7.8.

x�

�2

or

x�

1x

��

1 o

r x

�2

Sol

ve e

ach

com

pou

nd

in

equ

alit

y.T

hen

gra

ph

th

e so

luti

on s

et.

9.m

�3

�5

and

m�

3 �

710

.y�

5 �

�4

or y

�5

�1

{m2

�m

�4}

{yy

�1

or

y�

6}

11.4

�f

�6

and

f�

6 �

512

.w�

3 �

0 or

w�

7 �

9{f

�2

�f

��

1}{w

w�

�3

or

w�

2}

13.�

6 �

b�

4 �

214

.p�

2 �

�2

or p

�2

�1

{b�

2 �

b�

6}{p

p�

0 o

r p

�3}

Def

ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.15

–17.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

15.A

nu

mbe

r pl

us

one

is g

reat

er t

han

neg

ativ

e fi

ve a

nd

less

th

an t

hre

e.�

5 �

n�

1 �

3;{n

�6

�n

�2}

16.A

nu

mbe

r de

crea

sed

by t

wo

is a

t m

ost

fou

r or

at

leas

t n

ine.

n�

2 �

4 o

r n

�2

�9;

{nn

�6

or

n�

11}

17.T

he

sum

of

a n

um

ber

and

thre

e is

no

mor

e th

an e

igh

t or

is

mor

e th

an t

wel

ve.

n�

3 �

8 o

r n

�3

�12

;{n

n�

5 o

r n

�9}�

3�

4�

2�

10

12

34

�2

�1

01

23

45

6

�3

�4

�2

�1

01

23

4�

4�

3�

2�

10

12

34

�2

�1

01

23

45

6�

2�

10

12

34

56

�4

�3

�2

�1

01

23

4�

4�

3�

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10

12

34

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23

45

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78

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lenc

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lgeb

ra 1

Gra

ph

th

e so

luti

on s

et o

f ea

ch c

omp

oun

d i

neq

ual

ity.

1.�

4 �

e�

12.

x�

0 or

x�

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3.g

��

3 or

g�

44.

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te a

com

pou

nd

in

equ

alit

y fo

r ea

ch g

rap

h.

5.6.

x�

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ve e

ach

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y.T

hen

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ph

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e so

luti

on s

et.

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k�

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ine

a va

riab

le,w

rite

an

in

equ

alit

y,an

d s

olve

eac

h p

rob

lem

.Th

en c

hec

k y

our

solu

tion

.13

–14.

Sam

ple

an

swer

:L

et n

�th

e n

um

ber

.

13.T

wo

tim

es a

nu

mbe

r pl

us

one

is g

reat

er t

han

fiv

e an

d le

ss t

han

sev

en.

5 �

2n�

1 �

7;{n

2 �

n�

3}14

.A n

um

ber

min

us

one

is a

t m

ost

nin

e,or

tw

o ti

mes

th

e n

um

ber

is a

t le

ast

twen

ty-f

our.

n�

1 �

9 o

r 2n

�24

;{n

n�

10 o

r n

�12

}

MET

EOR

OLO

GY

For

Exe

rcis

es 1

5 an

d 1

6,u

se t

he

foll

owin

g in

form

atio

n.

Str

ong

win

ds c

alle

d th

e pr

evai

lin

g w

este

rlie

s bl

ow f

rom

wes

t to

eas

t in

a b

elt

from

40°

to60

°la

titu

de i

n b

oth

th

e N

orth

ern

an

d S

outh

ern

Hem

isph

eres

.

15.W

rite

an

in

equ

alit

y to

rep

rese

nt

the

lati

tude

of

the

prev

aili

ng

wes

terl

ies.

{w4

0 �

w�

60}

16.W

rite

an

in

equ

alit

y to

rep

rese

nt

the

lati

tude

s w

her

e th

e pr

evai

lin

g w

este

rlie

s ar

e n

otlo

cate

d.{w

w�

40 o

r w

�60

}

17.N

UTR

ITIO

NA

coo

kie

cont

ains

9 g

ram

s of

fat

.If

you

eat

no f

ewer

tha

n 4

and

no m

ore

than

7 co

okie

s,ho

w m

any

gram

s of

fat

will

you

con

sum

e?b

etw

een

36

g a

nd

63

g in

clu

sive

�2

�1

01

23

45

6�

2�

1�

4�

30

12

34

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01

23

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10

12

34

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01

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10

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34

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45

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23

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e (

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rag

e)

So

lvin

g C

om

po

un

d In

equ

alit

ies

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csS

olv

ing

Co

mp

ou

nd

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4

©G

lenc

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cGra

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ill36

5G

lenc

oe A

lgeb

ra 1

Lesson 6-4

Pre-

Act

ivit

yH

ow a

re c

omp

oun

d i

neq

ual

itie

s u

sed

in

tax

tab

les?

Rea

d th

e in

trod

uct

ion

to

Les

son

6-4

at

the

top

of p

age

339

in y

our

text

book

.

•E

xpla

in w

hy

it i

s po

ssib

le t

hat

Mr.

Kel

ly’s

in

com

e is

$41

,370

.

$41,

370

is g

reat

er t

han

or

equ

al t

o $

41,3

50 a

nd

less

th

an $

41,4

00.

•E

xpla

in w

hy

it i

s n

otpo

ssib

le t

hat

Mr.

Kel

ly’s

in

com

e is

$41

,400

.

$41,

400

is n

ot

less

th

an $

41,4

00.

Rea

din

g t

he

Less

on

1.W

hen

is

a co

mpo

un

d in

equ

alit

y co

nta

inin

g an

dtr

ue?

It is

tru

e w

hen

bo

th in

equ

alit

ies

are

tru

e.

2.T

he

grap

h o

f a

com

pou

nd

ineq

ual

ity

con

tain

ing

and

is t

he

of t

he

grap

hs

of t

he

two

ineq

ual

itie

s.

3.W

hen

is

a co

mpo

un

d in

equ

alit

y co

nta

inin

g or

tru

e?

It is

tru

e w

hen

on

e o

r b

oth

of

the

ineq

ual

itie

s is

tru

e.

4.T

he

grap

h o

f a

com

pou

nd

ineq

ual

ity

con

tain

ing

oris

th

e of

th

egr

aph

s of

th

e tw

o in

equ

alit

ies.

5.S

upp

ose

you

use

yel

low

to

show

th

e gr

aph

of

Ineq

ual

ity

#1 o

n t

he

nu

mbe

r li

ne.

You

use

blu

e to

sh

ow t

he

grap

h o

f In

equ

alit

y #2

.Wri

te a

nd

or o

rin

eac

h b

lan

k to

com

plet

e th

ese

nte

nce

.

a.T

he

part

th

at i

s gr

een

is

the

grap

h o

f In

equ

alit

y #1

In

equ

alit

y #2

.

b.

All

col

ored

par

ts f

orm

th

e gr

aph

of

Ineq

ual

ity

#1

Ineq

ual

ity

#2.

Hel

pin

g Y

ou

Rem

emb

er

6.O

ne

way

to

rem

embe

r so

met

hin

g is

to

con

nec

t it

to

som

eth

ing

that

is

fam

ilia

r to

you

.W

rite

tw

o tr

ue

com

pou

nd

stat

emen

ts a

bou

t yo

urs

elf,

one

usi

ng

the

wor

d an

dan

d th

eot

her

usi

ng

the

wor

d or

.

Sam

ple

an

swer

:I a

m 1

4 an

d I

am a

fre

shm

an in

hig

h s

cho

ol.

Aft

ersc

ho

ol,

I will

go

to

fo

otb

all p

ract

ice

or

I will

go

ho

me.

oran

d

un

ion

inte

rsec

tio

n

©G

lenc

oe/M

cGra

w-H

ill36

6G

lenc

oe A

lgeb

ra 1

So

me

Pro

per

ties

of

Ineq

ual

itie

sT

he

two

expr

essi

ons

on e

ith

er s

ide

of a

n i

neq

ual

ity

sym

bol

are

som

etim

es c

alle

d th

e fi

rst

and

seco

nd

mem

bers

of

the

ineq

ual

ity.

If t

he

ineq

ual

ity

sym

bols

of

two

ineq

ual

itie

s po

int

in t

he

sam

edi

rect

ion

,th

e in

equ

alit

ies

hav

e th

e sa

me

sen

se.F

or e

xam

ple,

a�

ban

d c

�d

hav

e th

e sa

me

sen

se;a

�b

and

c�

dh

ave

oppo

site

sen

ses.

In t

he

prob

lem

s on

th

is p

age,

you

wil

l ex

plor

e so

me

prop

erti

es

of i

neq

ual

itie

s.

Th

ree

of t

he

fou

r st

atem

ents

bel

ow a

re t

rue

for

all

nu

mb

ers

aan

d b

(or

a,b

,c,a

nd

d).

Wri

te e

ach

sta

tem

ent

in a

lgeb

raic

form

.If

the

stat

emen

t is

tru

e fo

r al

l n

um

ber

s,p

rove

it.

If i

t is

not

tru

e,gi

ve a

n e

xam

ple

to

show

th

at i

t is

fal

se.

1.G

iven

an

in

equ

alit

y,a

new

an

d eq

uiv

alen

t in

equ

alit

y ca

n b

ecr

eate

d by

in

terc

han

gin

g th

e m

embe

rs a

nd

reve

rsin

g th

e se

nse

.If

a�

b,t

hen

b�

a.a

�b

,a�

b�

0,�

b�

�a,

(�1)

(�b

) �

(�1)

(�a)

,b�

a

2.G

iven

an

ineq

uali

ty,a

new

and

equ

ival

ent

ineq

uali

ty c

an b

e cr

eate

dby

cha

ngin

g th

e si

gns

of b

oth

term

s an

d re

vers

ing

the

sens

e.If

a�

b,t

hen

2a

�2b

.a

�b

,a�

b�

0,�

b�

�a,

�a

��

b

3.G

iven

tw

o in

equ

alit

ies

wit

h t

he

sam

e se

nse

,th

e su

m o

f th

eco

rres

pon

din

g m

embe

rs a

re m

embe

rs o

f an

equ

ival

ent

ineq

ual

ity

wit

h t

he

sam

e se

nse

.If

a�

ban

d c

�d

,th

en a

�c

�b

�d

.a

�b

and

c �

d,s

o (

a�

b)

and

(c

�d

) ar

e p

osi

tive

nu

mb

ers,

so t

he

sum

(a

�b

) �

(c�

d)

is a

lso

po

siti

ve.

a�

b�

c�

d�

0,so

a�

c�

b�

d.

4.G

iven

tw

o in

equ

alit

ies

wit

h t

he

sam

e se

nse

,th

e di

ffer

ence

of

the

corr

espo

ndi

ng

mem

bers

are

mem

bers

of

an e

quiv

alen

t in

equ

alit

yw

ith

th

e sa

me

sen

se.

If a

�b

and

c�

d,t

hen

a�

c�

b�

d.T

he

stat

emen

t is

fal

se.5

�4

and

3 �

2,bu

t 5

�3

�4

�2.

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4



Stu

dy G

uid

e a

nd I

nte

rven

tion

So

lvin

g O

pen

Sen

ten

ces

Invo

lvin

g A

bso

lute

Val

ue

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-5

6-5

©G

lenc

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w-H

ill36

7G

lenc

oe A

lgeb

ra 1

Lesson 6-5

Ab

solu

te V

alu

e Eq

uat

ion

sW

hen

sol

vin

g eq

uat

ion

s th

at i

nvo

lve

abso

lute

val

ue,

ther

ear

e tw

o ca

ses

to c

onsi

der.

Cas

e 1:

Th

e va

lue

insi

de t

he

abso

lute

val

ue

sym

bols

is

posi

tive

.C

ase

2:T

he

valu

e in

side

th

e ab

solu

te v

alu

e sy

mbo

ls i

s n

egat

ive.

Sol

ve

x�

4�

1.T

hen

grap

h t

he

solu

tion

set

.

Wri

te

x�

4 �

1as

x�

4 �

1 or

x�

4 �

�1.

x�

4 �

1or

x�

4 �

�1

x�

4 �

4 �

1 �

4x

�4

��

1x

��

3x

�4

�4

��

1�4

x�

�5

Th

e so

luti

on s

et i

s {�

5,�

3}.

Th

e gr

aph

is

show

n b

elow

.

�8

�7

�6

�5

�4

�3

�2

�1

0

Wri

te a

n i

neq

ual

ity

invo

lvin

g ab

solu

te v

alu

e fo

r th

e gr

aph

.

Fin

d th

e po

int

that

is

the

sam

e di

stan

cefr

om �

2 as

it

is f

rom

4.

Th

e di

stan

ce f

rom

1 t

o �

2 is

3 u

nit

s.T

he

dist

ance

fro

m 1

to

4 is

3 u

nit

s.S

o,x

�1

�3.

10

�1

�2

�3

23

3 un

its3

units

45

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�2

�1

01

23

45

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ple1

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ple1

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ple2

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ple2

Exer

cises

Exer

cises

Sol

ve e

ach

op

en s

ente

nce

.Th

en g

rap

h t

he

solu

tion

set

.

1.y

�

3{�

3,3}

2.x

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100

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. 3x�

�6

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For

eac

h g

rap

h,w

rite

an

op

en s

ente

nce

in

volv

ing

abso

lute

val

ue.

13.

14.

15.

x

�4

x�

1 �

2x

�3

�4

�3

�4

�5

�6

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01

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01

23

40

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24

68

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01

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45

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20

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lenc

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ill36

8G

lenc

oe A

lgeb

ra 1

Ab

solu

te V

alu

e In

equ

alit

ies

Wh

en s

olvi

ng

ineq

ual

itie

s th

at i

nvo

lve

abso

lute

val

ue,

ther

e ar

e tw

o ca

ses

to c

onsi

der

for

ineq

ual

itie

s in

volv

ing

�(o

r �

) an

d tw

o ca

ses

to c

onsi

der

for

ineq

ual

itie

s in

volv

ing

�(o

r �

).

Rem

embe

r th

at i

neq

ual

itie

s w

ith

an

dar

e re

late

d to

in

ters

ecti

ons,

wh

ile

ineq

ual

itie

s w

ith

or

are

rela

ted

to u

nio

ns.

Sol

ve |

3a�

4| �

10.T

hen

gra

ph

th

e so

luti

on s

et.

Wri

te

3a�

4�

10 a

s 3a

�4

�10

an

d 3a

�4

��

10.

3a�

4 �

10an

d3a

�4

��

103a

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�4

�10

�4

3a�

4 �

4 �

�10

�4

3a�

63a

��

14

��

a�

2a

��

4

Th

e so

luti

on s

et i

s �a

�4

�a

�2 �.

Sol

ve e

ach

op

en s

ente

nce

.Th

en g

rap

h t

he

solu

tion

set

.

1.c

�2

�6

2.x

�9

�0

3.3

f�

10

�4

{cc

��

4 o

r c

�8}

��f

�4

�f

��

2 �

4.x

�

25.

x

�3

6.2

x�

1�

�2

{x�

2 �

x�

2}{x

x�

�3

or

x�

3}{x

xis

a r

eal n

um

ber

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6-5

6-5



Readin

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Lesson 6-5

Pre-

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6-5

6-5



An

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6-6

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4G

lenc

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Solv

e R

eal-

Wo

rld

Pro

ble

ms

Wh

en s

olvi

ng

real

-lif

e in

equ

alit

ies,

the

dom

ain

an

dra

nge

of

the

ineq

ual

ity

are

ofte

n r

estr

icte

d to

non

neg

ativ

e n

um

bers

or

to w

hol

e n

um

bers

.

BA

NK

ING

A b

ank

off

ers

4.5%

an

nu

al i

nte

rest

on

reg

ula

r sa

vin

gsac

cou

nts

an

d 6

% a

nn

ual

in

tere

st o

n c

erti

fica

tes

of d

epos

it (

CD

).If

Mar

jean

wan

tsto

ear

n a

t le

ast

$300

in

tere

st p

er y

ear,

how

mu

ch m

oney

sh

ould

sh

e d

epos

it i

nea

ch t

ype

of a

ccou

nt?

Let

x�

the

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nt

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site

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lar

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ngs

acc

oun

t.L

et y

�th

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t de

posi

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.T

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an

ope

n s

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nce

re

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ng

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sit

uat

ion

.

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ve f

or y

in t

erm

s of

x.

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ualit

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ivid

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ch s

ide

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ph y

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x�

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an

d te

st t

he

poin

t (0

,0).

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ce 0

��

0.75

(0)

�50

00 i

s fa

lse,

shad

e th

e h

alf-

plan

e th

at d

oes

not

con

tain

(0,

0).

On

e so

luti

on i

s (4

000,

2000

).T

his

rep

rese

nts

$40

00

depo

site

d at

4.5

% a

nd

$2,0

00 d

epos

ited

at

6%.

1.SO

CIA

L EV

ENTS

Tic

kets

for

th

e sc

hoo

l pl

ay c

ost

$5 p

er

stu

den

t an

d $7

per

adu

lt.T

he

sch

ool

wan

ts t

o ea

rn a

t le

ast

$5,4

00 o

n e

ach

per

form

ance

.

a.W

rite

an

in

equ

alit

y th

at r

epre

sen

ts t

his

sit

uat

ion

.5x

�7y

�54

00

b.G

raph

th

e so

luti

on s

et.

c.If

500

adu

lt t

icke

ts a

re s

old,

wh

at i

s th

e m

inim

um

nu

mbe

r of

stu

den

t ti

cket

s th

at m

ust

be

sold

?38

0

2.M

AN

UFA

CTU

RIN

GA

n a

uto

par

ts c

ompa

ny

can

pro

duce

525

fou

r-cy

lin

der

engi

nes

or

270

V-6

en

gin

es p

er d

ay.I

t w

ants

to

prod

uce

up

to 3

00,0

00 e

ngi

nes

per

yea

r.

a.W

rite

an

in

equ

alit

y th

at r

epre

sen

ts t

his

sit

uat

ion

.52

5f�

270s

�30

0000

b.A

re t

her

e re

stri

ctio

ns

on t

he

dom

ain

or

ran

ge?

Nei

ther

fn

or

sis

neg

ativ

e.

3.G

EOM

ETRY

Th

e pe

rim

eter

of

a re

ctan

gula

r lo

t is

les

s th

an 8

00 f

eet.

Wri

te a

nin

equ

alit

y th

at r

epre

sen

ts t

he

amou

nt

of f

enci

ng

that

wil

l en

clos

e th

e lo

t.2�

�2w

�80

0

Tick

et

Sale

s

Stu

den

t Ti

cket

s

Adult Tickets

300

060

090

0x

y

900

600

300

Inte

rest

on

Acc

ou

nts

Reg

ula

r Sa

vin

gs

Acc

ou

nt

($)

CD Account ($)

2000

040

0060

00x

y

6000

4000

2000

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Gra

ph

ing

Ineq

ual

itie

s in

Tw

o V

aria

bles

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-6

6-6

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

Gra

ph

ing

Ineq

ual

itie

s in

Tw

o V

aria

bles

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-6

6-6

©G

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w-H

ill37

5G

lenc

oe A

lgeb

ra 1

Lesson 6-6

Det

erm

ine

wh

ich

ord

ered

pai

rs a

re p

art

of t

he

solu

tion

set

for

eac

h i

neq

ual

ity.

1.y

�3x

,{(1

,5),

(1,0

),(�

1,0)

,(5,

1)}

{(1,

5),(

�1,

0)}

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ch e

ach

in

equ

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y w

ith

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ph

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6G

lenc

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Det

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wh

ich

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ered

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rs a

re p

art

of t

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solu

tion

set

for

eac

h i

neq

ual

ity.

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3),(

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}

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}

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ch e

ach

in

equ

alit

y w

ith

its

gra

ph

.

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da.

b.

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c

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7.x

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c.d

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ph

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ity.

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810

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11. M

OV

ING

A m

ovin

g va

n h

as a

n i

nte

rior

hei

ght

of 7

fee

t (8

4 in

ches

).Yo

u h

ave

boxe

s in

12 i

nch

an

d 15

in

ch h

eigh

ts,a

nd

wan

t to

sta

ck t

hem

as

hig

h a

s po

ssib

le t

o fi

t.W

rite

an

ineq

ual

ity

that

rep

rese

nts

th

is s

itu

atio

n.

12x

�15

y�

84

BU

DG

ETIN

GF

or E

xerc

ises

12

and

13,

use

th

e fo

llow

ing

info

rmat

ion

.

Sat

chi

fou

nd

a u

sed

book

stor

e th

at s

ells

pre

-ow

ned

vid

eos

and

CD

s.V

ideo

s co

st $

9 ea

ch,a

nd

CD

s co

st $

7 ea

ch.S

atch

i ca

n s

pen

d n

o m

ore

than

$35

.

12.W

rite

an

in

equ

alit

y th

at r

epre

sen

ts t

his

sit

uat

ion

.9x

�7y

�35

13.D

oes

Sat

chi

hav

e en

ough

mon

ey t

o bu

y 2

vide

os a

nd

3 C

Ds?

No

,th

e p

urc

has

es w

ill b

e $3

9,w

hic

h is

gre

ater

th

an $

35.

x

y

O

x

y

O

x

y

O

x

y

O

x

y

O

x

y O

x

y

O

Pra

ctic

e (

Ave

rag

e)

Gra

ph

ing

Ineq

ual

itie

s in

Tw

o V

aria

bles

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-6

6-6



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csG

rap

hin

g In

equ

alit

ies

in T

wo

Var

iabl

es

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-6

6-6

©G

lenc

oe/M

cGra

w-H

ill37

7G

lenc

oe A

lgeb

ra 1

Lesson 6-6

Pre-

Act

ivit

yH

ow a

re i

neq

ual

itie

s u

sed

in

bu

dge

ts?

Rea

d th

e in

trod

uct

ion

to

Les

son

6-6

at

the

top

of p

age

352

in y

our

text

book

.

Wh

at d

o 3

and

4 re

pres

ent

in t

he

term

s 3x

and

4y?

the

aver

age

amo

un

t sp

ent

on

a c

afet

eria

lun

ch a

nd

a

fast

-fo

od

lun

ch

Rea

din

g t

he

Less

on

1.C

ompl

ete

the

char

t to

sh

ow w

hic

h t

ype

of l

ine

is n

eede

d fo

r ea

ch s

ymbo

l.

Sym

bo

lTy

pe

of

Lin

eB

ou

nd

ary

Par

t o

f S

olu

tio

n?

�d

ash

edn

o

�d

ash

edn

o

�so

lidye

s

�so

lidye

s

2.If

a t

est

poin

t re

sult

s in

a f

alse

sta

tem

ent,

wh

at d

o yo

u k

now

abo

ut

the

grap

h?

Th

e h

alf-

pla

ne

con

tain

ing

th

e te

st p

oin

t is

no

t p

art

of

the

solu

tio

n a

nd

is

no

t sh

aded

.

3.If

a t

est

poin

t re

sult

s in

a t

rue

stat

emen

t,w

hat

do

you

kn

ow a

bou

t th

e gr

aph

?

Th

e h

alf-

pla

ne

con

tain

ing

th

e te

st p

oin

t is

par

t o

f th

e so

luti

on

an

d

is s

had

ed.

4.W

hen

can

th

e or

igin

not

be u

sed

as a

tes

t po

int?

Th

e o

rig

in c

ann

ot

be

use

d a

s a

test

po

int

wh

en it

is o

n t

he

bo

un

dar

y.

Hel

pin

g Y

ou

Rem

emb

er

5.T

he

two-

vari

able

in

equ

alit

ies

in t

his

les

son

can

be

solv

ed f

or y

in t

erm

s of

xto

get

ase

nte

nce

in

slo

pe-i

nte

rcep

t fo

rm.I

t lo

oks

mu

ch l

ike

a sl

ope-

inte

rcep

t eq

uat

ion

,bu

t it

has

an i

neq

ual

ity

sym

bol

inst

ead

of a

n e

qual

s si

gn.F

or e

xam

ple,

4x�

2y�

5 ca

n b

e w

ritt

en

as y

��

2x�

.Exp

lain

how

to

grap

h a

n i

neq

ual

ity

once

it

is w

ritt

en i

n s

lope

-in

terc

ept

form

.Use

th

e id

ea t

hat

gre

ater

can

mea

n a

bove

and

less

can

mea

n b

elow

.

Dra

w t

he

bo

un

dar

y lin

e.If

th

e in

equ

alit

y sy

mb

ol i

s �

or

�,m

ake

the

bo

un

dar

y d

ash

ed.I

f th

e sy

mb

ol i

s �

or

�,m

ake

the

bo

un

dar

y lin

e so

lid.

If t

he

sym

bo

l in

th

e sl

op

e-in

terc

ept

ineq

ual

ity

is �

or

�,s

had

e b

elo

w t

he

bo

un

dar

y to

ind

icat

e sm

alle

r va

lues

of

y.If

th

e sy

mb

ol i

s �

or

�,s

had

eab

ove

the

bo

un

dar

y to

ind

icat

e g

reat

er v

alu

es o

f y.

5 � 2

©G

lenc

oe/M

cGra

w-H

ill37

8G

lenc

oe A

lgeb

ra 1

Usi

ng

Eq

uat

ion

s:Id

eal W

eig

ht

You

can

fin

d yo

ur

idea

l w

eigh

t as

fol

low

s.

A w

oman

sh

ould

wei

gh 1

00 p

oun

ds f

or t

he

firs

t 5

feet

of

hei

ght

and

5 ad

diti

onal

pou

nds

for

eac

h i

nch

ove

r 5

feet

(5

feet

�60

in

ches

).A

man

sh

ould

wei

gh 1

06 p

oun

ds f

or t

he

firs

t 5

feet

of

hei

ght

and

6 ad

diti

onal

pou

nds

for

eac

h i

nch

ove

r 5

feet

.Th

ese

form

ula

s ap

ply

tope

ople

wit

h n

orm

al b

one

stru

ctu

res.

To

dete

rmin

e yo

ur

bon

e st

ruct

ure

,wra

p yo

ur

thu

mb

and

inde

x fi

nge

rar

ound

the

wri

st o

f yo

ur o

ther

han

d.If

the

thu

mb

and

fing

er ju

st t

ouch

,yo

u h

ave

nor

mal

bon

e st

ruct

ure

.If

they

ove

rlap

,you

are

sm

all-

bon

ed.

If t

hey

don

’t ov

erla

p,yo

u a

re l

arge

-bon

ed.S

mal

l-bo

ned

peo

ple

shou

ldde

crea

se t

hei

r ca

lcu

late

d id

eal

wei

ght

by 1

0%.L

arge

-bon

ed p

eopl

esh

ould

in

crea

se t

he

valu

e by

10%

.

Cal

cula

te t

he

idea

l w

eigh

ts o

f th

ese

peo

ple

.

1.w

oman

,5 f

t 4

in.,

nor

mal

-bon

ed2.

man

,5 f

t 11

in

.,la

rge-

bon

ed12

0 lb

189.

2 lb

3.m

an,6

ft

5 in

.,sm

all-

bon

ed4.

you

,if

you

are

at

leas

t 5

ft t

all

187.

2 lb

An

swer

s w

ill v

ary.

For

Exe

rcis

es 5

–9,u

se t

he

foll

owin

g in

form

atio

n.

Su

ppos

e a

nor

mal

-bon

ed m

an i

s x

inch

es t

all.

If h

e is

at

leas

t 5

feet

tall

,th

en x

�60

rep

rese

nts

th

e n

um

ber

of i

nch

es t

his

man

is

over

5

feet

tal

l.F

or e

ach

of

thes

e in

ches

,his

ide

al w

eigh

t is

in

crea

sed

by

6 po

un

ds.T

hu

s,h

is p

rope

r w

eigh

t (y

) is

giv

en b

y th

e fo

rmu

la

y�

6(x

�60

) �

106

or y

�6x

�25

4.If

th

e m

an i

s la

rge-

bon

ed,t

he

form

ula

bec

omes

y�

6x�

254

�0.

10(6

x�

254)

.

5.W

rite

th

e fo

rmu

la f

or t

he

wei

ght

of a

lar

ge-b

oned

man

in

slo

pe-

inte

rcep

t fo

rm.

y�

6.6x

�27

9.4

6.D

eriv

e th

e fo

rmu

la f

or t

he

idea

l w

eigh

t (y

) of

a n

orm

al-b

oned

fem

ale

wit

h h

eigh

t x

inch

es.W

rite

th

e fo

rmu

la i

n

slop

e-in

terc

ept

form

.y

�5x

�20

0

7.D

eriv

e th

e fo

rmu

la i

n s

lope

-in

terc

ept

form

for

th

e id

eal

wei

ght

(y)

of a

lar

ge-b

oned

fem

ale

wit

h h

eigh

t x

inch

es.

y�

5.5x

�22

0

8.D

eriv

e th

e fo

rmu

la i

n s

lope

-in

terc

ept

form

for

th

e id

eal

wei

ght

(y)

of a

sm

all-

bon

ed m

ale

wit

h h

eigh

t x

inch

es.

y�

5.4x

�22

8.6

9.F

ind

the

hei

ghts

at

wh

ich

nor

mal

-bon

ed m

ales

an

d la

rge-

bon

edfe

mal

es w

ould

wei

gh t

he

sam

e.68

in.,

or

5 ft

8 in

.

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-6

6-6



1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. B

D

B

B

A

D

D

A

B

A

C

�1

B

B

D

A

C

D

A

D

B

C

B

D

D

A

D

B

D

B

C

A

Chapter 6 Assessment Answer Key Form 1 Form 2APage 379 Page 380 Page 381



12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: {x ��3 � x � 4}

A

B

B

C

B

D

C

A

D

B

B

C

B

A

D

D

D

B

A

A

{�12, 12}

D

D

A

A

C

C

C

A

D

Chapter 6 Assessment Answer KeyForm 2A (continued) Form 2BPage 382 Page 383 Page 384

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:�3 1 117

y

xO

(0, �4)

(3, �2)

y

xO

�w ��3 � w � 2�13

��{�2, 1.5}

�1�2�3�4 0 1 2 43

{x �x � 1 or x � 2}

�1�2�3�4 0 1 2 43

{�1, 3}

�1�2�3�4 0 1 2 43

�2 0 2 4 86

{b ��2 � b � 7}0

{x �x is a real number}

�1�2�3�4�5�6 0 1 2

{w ��5 � w � 2}

{c �c � 13}

{p �p � 2}

{x �x � 8}

{a �a � 9}

{r �r � �5.5}

{y �y � �5.5}

{t �t � 84}

�b�b � �1�35

��

{z �z � �4}

{t �t � 6}

�17�19�21 �15

{n�n � �19}131211109 14 15 1716

{x �x � 13}

Chapter 6 Assessment Answer KeyForm 2CPage 385 Page 386

Sample answer:n � the number;2 n � 7; {n�n � 5}

Sample answer:n � the number of checks;3.5 � 2.5 0.1n � 5;Between 10 and 25 checks.

3x 0.75y � 20;No, the costwould be morethan $20.00.


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:�7 �5 3 5

y

xO

y

xO

(0, 0)

(1, 3)

�c � c � ��13

� or c � 3�

{1, 4}

�1�2�3 0 1 2 4 53

{w ��3 � w � 5}�11 30

{�11, 3}

�1�2�3�4 0 1 2 43

{x �x � 2}�1�2 0 1 2 4 5 63

{y � 0.5 � y � 4}0

{w � w is a real number.}

�1�2�3�4 0 1 2 43

{w � 2 � w � 3}

{x � x � �11}

{w � w � �5}

{t � t � �5.5}

{f � f � 0.25}

{m � m � 6}

{k � k � 3.5}

�z � z � �3�13

��{h � h � 27}

{k �k � 5}

{s�s � 9}

�7�9�11 �5

{m�m � �9}1312111098 14 15 16

{y �y � 12}

Chapter 6 Assessment Answer KeyForm 2DPage 387 Page 388

An

swer

s

Sample answer:n � the number ofchecks;5.75 � 3.75 0.1n � 7.25;Between 20 and 35 checks.

28x 4y � 75;No, the costwould be morethan $75.00.

Sample answer:n � the number;14 � n 5; {n � n � 9}


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

16x 12y � 120; 3

y

xO

(0, 0)

(1, �3)

�1�2 0 1 2 4 5 63

{x �x � �1 or x � 4}

�1�2 0 1 2 4 5 63

{x ��2 � x � 6}

�2.8 40

{�2.8, 4}

�6 80

{x ��6 � x � 8}

�1�2�3�4�5�6�7�8�9

{n�n � �6}

0

{x � x � �9}

{b � b � 0.5}

�t � t � �191��

{w � w � �10.4}

3635343332 37 38 4039

{t � t � 36}

9.3

{m�m � 9.3}

Chapter 6 Assessment Answer KeyForm 3Page 389 Page 390

Sample answer:n � the number;n � 15 � 2n 8;{n � n � �23}

Sample answer:n � the number;

��37

� n � 2;

�n � n � 2�37

��

Sample answer:j � cost of jeans;2(19.89) j � 78;no more than $38.22Sample answer:n � small positiveeven integer;n n 2 � 15;6, 8; 4, 6; 2, 4

Sample answer:s � amount of sales;32,500 � 0.1s 25,600 �41,900 between $69,000and $163,000

false; Sample answer:x � 3 and y � 1.If xy � 0, x and ycannot both bepositive so x � 3 andy � 1 is false.

Chapter 6 Assessment Answer KeyPage 391, Open-Ended Assessment

Scoring Rubric


Score General Description Specific Criteria

• Shows thorough understanding of the concepts of usingthe properties of inequalities, solving inequalities, solvingcompound inequalities, solving open sentences involvingabsolute value, and graphing inequalities in two variables.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.

• Shows an understanding of the concepts of using theproperties of inequalities, solving inequalities, solvingcompound inequalities, solving open sentences involvingabsolute value, and graphing inequalities in two variables.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts of usingthe properties of inequalities, solving inequalities, solvingcompound inequalities, solving open sentences involvingabsolute value, and graphing inequalities in two variables.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of most of the concepts ofusing the properties of inequalities, solving inequalities,solving compound inequalities, solving open sentencesinvolving absolute value, and graphing inequalities in twovariables.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

4 SuperiorA correct solution that is supported by well-developed, accurateexplanations

An

swer

s


Chapter 6 Assessment Answer KeyPage 391, Open-Ended Assessment

Sample Answers

2a. After drawing a graph, studentsshould write an inequality thatcorresponds with the line they havedrawn. The inequality may or may notinclude equality.

2b. The solution set includes the boundary(line) if the inequality written for parta includes equality. If the inequalitywritten for part a does not includeequality, then the student should statethat the solution set of the inequalitydoes not include the line.

3. The inequality ab � 2a can bedetermined to be true or false byconsidering the value of a. Since b � 2,by the Multiplication Property ofInequality ab � 2a is true if a is apositive number.

4a. � x � � 3 means the distance from 0 to xis 3 units. The only values for x thatsatisfy this statement are x � �3 andx � 3. Thus, the solution set is {�3, 3}.

4b. The solution set for � x � 2 � � 4 is {x � x � �2 or x � 6}. The solution setfor �2x � 4 or x � 6 is {x � x � �2}.One includes numbers greater than�2, and the other includes numbersless than �2 or greater than 6. Thesesolution sets are not the same.

5a. w � 90 � 2(20); {w � w � 50}5b. The formula for the area of a rectangle

with 50 substituted for the width can be used to write the compound inequality 2800 � 50� � 3200. The possiblelengths are found by solving thiscompound inequality for �. Thesolution set is {� � 56 � � � 64}.

5c. � 175,000 � x � � 20,000;155,000 � x � 195,000;The Fraziers are willing to pay from$155,000 to $195,000 for the house.

In addition to the scoring rubric found on page A25, the following sample answers may be used as guidance in evaluating open-ended assessment items.

1. 10n � 7(n � 2) � 5n � 12 Original inequality10n � 7n � 14 � 5n � 12 Distributive Property

3n � 14 � 5n � 12 Combine like terms.3n � 14 � 5n � 5n � 12 � 5n Subtract 5n from each side.

�2n � 14 � �12 Simplify.�2n � 14 � 14 � �12 � 14 Add 14 to each side.

�2n � 2 Simplify.

��22n

� � 2 (�2) Divide each side by �2.

n � �1 Simplify.

The solution set is {n�n � �1}.


1. true

2. false; equation

3. false; or

4. false; negative

5. true

6. true

7. false; positive

8. true

9. true

10. false; intersection

11. Multiply both sidesof the inequality by

��32

� and change �

to �.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lesson 6–3)

Page 393

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

Quiz (Lesson 6–6)

Page 394

1.

2.

3.

4. 35x 25y � 230;No, the cost isgreater than $230.

y

xO

{(0, 1), (�1, 2)}

�x � � 1

{�4, �1}

0 1 2 4 5 6 7 83

{y �y � 5 or y � 6}

�1�2�3�4�5�6 0 1 2

{x ��5 � x � 0}

{y � y � 1}

{y � y � 3}

{d � d � �100}

B

{w �w � �2.3}

{n � n � �28}

�r � r � 1�115��

{m � m � �78}

�m�m � �12

��{r � r � 0}

13121110 14 15 17 1816

{w � w � �14}13121110 14 15 17 1816

{n � n � 14}

Chapter 6 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 6–1 and 6–2) Quiz (Lessons 6–4 and 6–5)

Page 392 Page 393 Page 394

An

swer

s

Sample answer:n � the number;n 3 � 19 � n; {n � n � 8}

Sample answer:n � the number;n � 7 � 15; {n � n � 22}

Sample answer:x � the number;16 � 8x � 40; {x � 2 � x � 5}

y

xO


1.

2.

3.

4.

5.

6.

7.

8.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

�1�2�3�4 0 1 2 43

�x � �3 � x � �13

��;

let n � the number;2n � 7 � �5 or 2n � 7 � 13;{n � n � 1 or n � 10}

{u � u � 18}

�1�2�3�4 0 1 2 43

{r � r � 3};

y

xO 1

123456789

2 3 4 5 6 7 8 9

y � 3x 5

d � 55t; 275 miles

��87

�

yes; common difference is 3

{(1, �2), (�1, 3), (�2, 2), (0, �2)}

X

�2

3

�10

�1�22

Y

decrease; 25%

�29

�

whole number, integer,rational number

32y 38

Sample answer:a � no. of apples;6a � 50;

at least 8�13

� apples

Sample answer:� � length; � 63 � 85;22 in. or less

�v � v � �49

��{t � t � 15.2}

C

B

D

C

Chapter 6 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 395 Page 396

negative correlation


1.

2.

3.

4.

5.

6.

7.

8.

9.

10. 11.

12. 13.

14.

15.

16. DCBA

DCBA

DCBA

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

2 5

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

8

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

. 7 56

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

7 / 2

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

Chapter 6 Assessment Answer KeyStandardized Test Practice

Page 397 Page 398

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20. B

B

C

D

A

B

C

C

D

B

A

B

D

A

C

B

C

D

A

D

Chapter 6 Assessment Answer KeyFirst Semester Test

Page 399 Page 400


21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47. {�10, 3}�4�3�2�1 0 2 3 4 5 6 71

{x � x � �2 or x � 5};

{x � x � �2}

{t � t � 3}

Sample answer using(4, 80) and (10, 29):

y � ��127�x � 114

negative correlation

1

�34

�; �2; �83

�

C � 1.9n

an � 4n � 3

y

xO

y � 2x – 3

{(�4, 2), (�4, �3),(0, �3), (2, 0), (3, 1)};

{(2, �4), (�3, �4),(�3, 0), (0, 2), (1, 3)}

dilation

310 mph

increase; 15%

�45

�

2

36

3:1

4.4

�28xy � 4uv

{�1, 0, 1, 2, 3, 4, 5, 6, …}

You could visit an artgallery that has no paintings by Monet.

1.8x � 10.9y

Additive InverseProperty; �5

{1, 2, 3}

11

An

swer

s


Chapter 6 Assessment Answer KeyFirst Semester Test (continued)

Page 401 Page 402

Chapter 6 Resource Masters - Morgan Park High …©Glencoe/McGraw-Hill iv Glencoe Algebra 1...

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