Post on 28-Jun-2020
I hope that you find this resource helpful in your classroom. Please feel free to contact me with any questions as you implement this in your class.
Maneuvering the Middle is an education blog with valuable tips for lesson planning, teacher organization, and math concepts in the middle school classroom.
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M A N E U V E R I N G T H E M I D D L E .C O M
PA G E T W O
PAGE TOPIC RESOURCE4 Sample Pacing Guide
5-6 Ideas for Implementation & Helpful Hints
7-16 Binder Covers, Dividers, and Spine Labels
17-18 Intro to Inequalities Student Handout 1
19 Intro to Inequalities Homework 1
21-22 Solving One-Step Inequalities Student Handout 2
23 Solving One-Step Inequalities Homework 2
25-26 Solving Two-Step Inequalities Student Handout 3
27 Solving Two-Step Inequalities Homework 3
29 Inequalities Quiz Quiz 1
31-32 Writing Inequalities Student Handout 4
33 Writing Inequalities Homework 4
35-36 Solving Inequalities in Real Life Student Handout 5
37 Solving Inequalities in Real Life Homework 5
39-46 Inequalities Unit Study Guide Study Guide
47-48 Inequalities Unit Test Test
INEQUALITIES UNITTable of Contents
©Maneuvering the Middle LLC, 2016
DAY 1 DAY 2 DAY 3 DAY 4 DAY 5
Intro to Inequalities Solving One-Step Inequalities
Solving Two-Step Inequalities
Inequalities Quiz Writing Inequalities
Student Handout 1Homework 1
Student Handout 2Homework 2
Student Handout 3Homework 3
Quiz 1 Student Handout 4Homework 4
DAY 6 DAY 7 DAY 8 NOTES
Solving Inequalities in Real Life
Inequalities UnitStudy Guide
Inequalities Unit Test
Student Handout 5Homework 5
Unit Study Guide Unit Test
©Maneuvering the Middle LLC, 2017
INEQUALITIESPACING GUIDE
*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy.
Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and help your students to be successful with inequalities. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included.
If you notice any discrepancies in the documents or have any questions, please email me at: support@maneuveringthemiddle.com.
STANDARDS7.EE.4 Use variables to represent quantities in a real-world or mathematical problems, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
• 7.EE.4B Solve word problems leading to inequalities of the form px + q> r or px +q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
INEQUALITIESStudent Handouts
©Maneuvering the Middle LLC, 2016
HELPFUL HINTS
A few ideas for organizing your curriculum and keeping things nice and neat:
Keep each unit in a separate binder and use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5” binders.
©Maneuvering the Middle LLC, 2016
Student Handouts
BINDERS
I place my originals in page protectors in chronological order. Any extra copies from that lesson, I hole punch and place behind that page. When I need an extra or a student is missing something from weeeeeeeeks ago, I can simply pull out a copy.
PAGE PROTECTORS
I highlight the edges of my answer keys or if I am really good, print them on colored paper. It helps them to stand out and makes them easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn’t show up if you make a copy.
ANSWER KEYS
Card stock in a page protector makes an awesome divider. When I set up my dividers, I include one for handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included. J
CARD STOCK
Happy Teaching!
INEQUALITIES
©MANEUVERINGTHEMIDDLE,2016
s e v e n t h G r a d e C u r r i c u l u m
U n i t f i v e : 7 . e e . 4
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©MANEUVERINGTHEMIDDLE,2016
INEQUALITIES
s e v e n t h G r a d e C u r r i c u l u m
U n i t F I V E : A N S W E R K E Y S
©MANEUVERINGTHEMIDDLE,2016
INEQUALITIES
s e v e n t h G r a d e C u r r i c u l u m
U n i t F I V E : A C T I V I T I E S
©MANEUVERINGTHEMIDDLE,2016
INEQUALITIES
s e v e n t h G r a d e C u r r i c u l u m
U n i t F I V E : A S S E S S M E N T S
1. k + 8 ≥ 19, if k = 11 2. 12 > f, if f = 3 3. 3 > d, if d = 3
4. c – 12 > 30, if c = 13 5. 16 < b – 8, if b = 22 6. 6x + 5 < 18, if x = 5
7. 2j ≤ 8, if j = 5 8. 5r – 3 ≥ 25, if r = 6 9. 6m – 12 < 40, if m = 8
Determine whether each value makes a true statement.
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesStudent Handout 1
INTRO TO INEQUALITIESAn equation uses an ______________ sign to show that both sides are _______________ .
An _________________ shows that both sides are ______ equal.
GREATER THAN GREATER THAN OR EQUAL TO LESS THAN LESS THAN OR
EQUAL TO NOT EQUAL
Use the _________________ as the starting point when reading inequalities.
©Maneuvering the Middle LLC, 2016
Use an inequality symbol to create a true statement.
a. 4 ____ 9 b. 0.5 ____ 0.45 c. -3 ____ -2 d. -6.1 ____ -6.10 e. 12.4 ____ 12.04
Write a verbal description to represent the inequality statements below.
6 ≤ x: ______________________________________________________________________________
y < 0.5: ____________________________________________________________________________
1 2 3 4 5-1 0 1 2 315 20 25 30 35
3 4 5 6 710 11 12 13 14
10. k > 11
11. 12 ≥ f
12. d < 6
13. c < 25
14. 0 ≤ b
15. x ≥ 4.5
8 9 10 11 12
Practice graphing the following inequalities.
Inequalities can also be _________________ on the ______________________ .
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
INCLUDED NOT INCLUDED
Based on the verbal expression below, write and graph an inequality.
16. The McDonald family spends no more than $150 for groceries each week.
17. Jerod earns at least $10 per hour when mowing lawns.
0 2 3 4 5 61 87 9
x≤ 5
8 9 10 11 12 10 11 12 13 14 3 4 5 6 7
7. k ≤ 8 8. 13.5 ≥ f 9. d < 4
4.
________
5.
________
6.
________
1. k + 12 ≥ 20, if k = 15 2. -16 > -f, if f = 15 3. 9 > d, if d = 3
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesHomework 1
©Maneuvering the Middle LLC, 2016
Based on the verbal expression below, write and graph an inequality.
10. The Parkland Zoo has a maximum capacity of 350 visitors (v).
11. Trina must spend at least 45 minutes (m) studying for her test.
INTRO TO INEQUALITIES
8 9 10 11 12 10 11 12 13 14 3 4 5 6 7
Substitute each variable to determine whether the inequality statement is true or false.
Write an inequality for each solution set graphed below.
Practice graphing the following inequalities:
2. c – 8 > 14 ✓ CHECK:
Name _____________________________________Date ______________________________Pd______
Unit: Inequalities Student Handout 2
SOLVING ONE-STEP INEQUALITIES
1. n + 5 ≤ 16 ✓ CHECK:
©Maneuvering the Middle LLC, 2016
Inequalities can be _______________just like an _______________, but with a few
exceptions. J
3. 12g < 48 ✓ CHECK: 4. p3
> 9 ✓ CHECK:
Solve each inequality, check your answer, and then graph the solution.
ONE-STEP INEQUALITIES
The goal when solving an inequality is to isolate the variable.
1. Isolate the variable by using ______________ or opposite
operations.
2. The inequality must remain ______________.
3. When you multiply or divide by a ______________number, the
inequality sign is ______________.
What observations can you make about the problems above?
Inequalities sometimes involve _________________numbers. Remember, when
multiplying or dividing by a ________________number, be sure to __________the sign.
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
7. -7x ≥ 35
_________
8.x – 16 < 11
_________
9.8 ≥ x + 10
_________
10.x8
> −3
_________
11.6x ≥ -108
_________
12.-15 ≤ x + 7
_________
Solve each inequality, check your answer, and then graph the solution.
5. -4k ≤ 22 ✓ CHECK: 6. s−2 > 5 ✓ CHECK:
Solve each inequality, and then graph your solution.
4. Which inequality is true when x = 4?
A. x + 5 ≤ 3
B. 9x > 36
C. x2
< 3
D. 18 ≤ x – 8
6. Jasmine is baking and selling cupcakes for $15 per dozen. She would like to make more than $120 in cupcake sales. Which number line below represents the solutions to this situation?
A.
B.
C.
D.
5. Which inequality is NOT true when x = -2?
A. 6x < -10
B. -2x > -3
C. x4
≤ 0
D. -4 ≤ x – 5
1.18 ≥ -2x
2.x
4≤ 8
3.x – 7 > -11
✔ CHECK: ✔ CHECK: ✔ CHECK:
Graph: Graph: Graph:
©Maneuvering the Middle LLC, 2016
Name _____________________________________Date ____________________________Pd ______
Unit: InequalitiesHomework 2
SOLVING ONE-STEP INEQUALITIESSolve the following one-step inequalities, check your work, and graph the solution.
Use your understanding of one-step inequalities to answer the questions below.
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
0 5 10 15 20
1.10 + 3k ≤ 22
2.19 > -4p – 5
3.1
2r + 3 < 6
✓ CHECK: ✓ CHECK: ✓ CHECK:
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesStudent Handout 3
SOLVING TWO-STEP INEQUALITIESTwo-step inequalities follow the same _______________for isolating the variable.
Think of it as “undoing” ______________.
Solve each two-step inequality below. Then, prove that your answer is correct.
5x + 9 < 17
SOLVING TWO-STEP
INEQUALITIES
1. Undo addition or subtraction with the ________________ operation.
2. Undo multiplication or ________________ with the inverse operation.
3. When you multiply or divide by a ______________number, the inequality
sign is ______________. (watch for negative signs)
3. Isolate the ________________.
4. Check the ________________ sign.
-2x – 3 > 13
©Maneuvering the Middle LLC, 2016
DICE ROLL SOLVE SOLUTION GRAPH
2 4x – 8 < 32
3 -6x + 9 ≤ 25
4 3
4x + 8 < 41
5 2.5 x – 10 > 25
6x
6 + 2 ≥ −16
7 -16 > 5 + 7x
8 6 + 1.5x < -12
9 -8x – 9 > -21
10 42 ≥ -6 + 3x
11 -10x + 25 ≤ 5
12 30 ≤ 3x – 5
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
Solve each equation below for practice. Roll a pair of dice, and find the sum of the two numbers showing. Solve that problem.
SHOW WORK HERE:
©Maneuvering the Middle LLC, 2016
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesHomework 3
Match each of the inequalities to their appropriate graph Record your results below.
MATCH 1 MATCH 4
MATCH 2 MATCH 5
MATCH 3 MATCH 6
E
3x – 1 < -10
SOLVING TWO-STEP INEQUALITIES
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesQuiz 1
QUIZ: INEQUALITIESMatch each of the following inequality statements to the appropriate graph.
1. x > 6.5
2. − 12
≥ x
3. 6.5 > x
4. x > − 12
Evaluate whether each value makes a true or false statement.
5. k+ 6 ≥ 19, if k = 11 6. 16 < b + 8, if b = 22
Solve each inequality below.
©Maneuvering the Middle LLC, 2016
Answers
1. ______________
2. ______________
3. ______________
4. ______________
5. ______________
6. ______________
7. ______________
8. ______________
9. _____________
10. _____________
11. _____________
12. _____________
7. -4x ≤ 32 8. 6x – 18 ≤ 27 9. x4
< -1.5
10. 5 + x2≥ 10 11. 10 + 2.5x > 35 12. 9 –x < -11
A.
B.
C.
D.
E.
-6 -4 -2 0 2
-1 1 3 5 7
2 4 6 8 10
-3 -2 -1 0 1
1 3 5 7 9
INEQUALITY PHRASES
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesStudent Handout 4
©Maneuvering the Middle LLC, 2016
WRITING INEQUALITIES
Verbal statements can be _________________ to algebraic inequalities, much like
deciphering a secret message or translating from one _________________ to another.
Translate each of the following into an algebraic inequality.
1. a number is at most fifteen 2. the sum of a number and three is less than twelve
3. the quotient of a number and negative two is greater than or equal to ten
4. four less than a number is at least negative six
5. the difference between a number and thirteen is atleast one
6. eight less a number is less than or equal to five
7. three times a number is more than negative seven
8. one-half of a number plus five is greater than eleven
9. negative six plus a number is less than or equal to fifteen
< > < >
Inequality: ___________________
Solution: _____________________
Graph:
Inequality: ___________________
Solution: _____________________
Graph:
Inequality: ___________________
Solution: _____________________
Graph:
Translate each statement into an algebraic inequality. Then, solve and graph the solution.
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
10. the sum of twice a number and four is at least 16
11. one-half of a number less six is greater than or equal to ten
12. three times a number increased by seven is less than eleven
13. the difference of two and a number is at least negative one
14. the quotient of a number and five is no greater than negative nine
15. twice a number less than twenty is at most ten
Inequality: ___________________
Solution: _____________________
Graph:
13. Which of the following inequality statements is represented by the graph below?
A. x – 2 ≤ 4 B. x2
+ 2 ≥ −6 C. -4 ≥ x D. x2≥ −2
Inequality: ___________________
Solution: _____________________
Graph:
Inequality: ___________________
Solution: _____________________
Graph:
-10 -8 -6 -4 -2
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesHomework 4
_______________ _________________________
1
Four more than three times a number is greater than twenty-two.
2
One less than five times a number is fewer than twenty-four.
3
Eight less a number is less than or equal to seventeen.
4
Negative ten is no less than two times a number plus fourteen.
WHAT IS A BIRD’S FAVORITE TYPE OF MATH?
L C G
W O I
B R P
A E D
4 8 1 6 5 3 7 2
©Maneuvering the Middle LLC, 2016
Match the phrases to the algebraic solution below. Then, write the letter in the blank below.
5
Twenty-seven is smaller than five times a number increased by seven.
6
A number divided by three less two is at most two.
7
The sum of eight times a number and negative four exceeds twelve.
8
The quotient of a number and negative one increased by eleven is less than or equal to fifteen.
x ≥ −4
5x < x < 6
x ≤12x > 3
x ≤ −12
x > 6
x ≥ −9 x > 2 x ≤ −9
x <11.5
x > 4
WRITING INEQUALITIES
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesStudent Handout 5
SOLVING INEQUALITIES IN REAL LIFE
I KNOW: I NEED TO KNOW:
PLAN AND WORK: MY SOLUTION:
I KNOW: I NEED TO KNOW:
PLAN AND WORK: MY SOLUTION:
1. Missy is saving to attend a week at summer camp. She needs $250.00 to register. Her
parents will contribute $75.00. She needs to raise the rest of the money babysitting for $12.00
per hour. What is the minimum number of hours she must babysit in order to attend camp?
2. The youth soccer team is fundraising by washing cars. They paid $84.55 for supplies. If they charge $8.00 per wash, how many cars must be washed to profit at least $300.00 dollars?
©Maneuvering the Middle LLC, 2016
Summarize today’s lesson:
I KNOW: I NEED TO KNOW:
PLAN AND WORK: MY SOLUTION:
I KNOW: I NEED TO KNOW:
PLAN AND WORK: MY SOLUTION:
3. JoAnn has a bank account with $350.00 in it. Every week, she withdraws $12.50 to attend the movies. What is the maximum number of weeks that JoAnn can withdraw the money without allowing her bank account to drop below $210.00?
4. A jet ski rental charges a flat rate of $75, plus an additional $60 per hour. You do not want to spend more than $200. How many hours can you rent the jet ski and still be under budget?
©Maneuvering the Middle LLC, 2016
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesHomework 5
Answer the following questions. Be sure to justify your responses.
©Maneuvering the Middle LLC, 2016
1. Marcus needs to bike at least 80 miles this week for his training. If he has already biked 25miles this week, then how many miles should he bike on each of the 5 remaining days this week?
Variable: ______________________________
Inequality: ______________________________
Solution: ______________________________
2. Jamal has $15.00 to spend at the concession stand. He buys nachos for $7.50, and he wants to purchase some Sour Straws for $1.50 each. How many Sour Straws can Jamal purchase with the money that he has?
Variable: ______________________________
Inequality: ______________________________
Solution: ______________________________
3. Taylor has a $30.00 gift card that she can spend at the store. She has already bought a $9.00 picture frame, and she wants to buy $3.00 journals with the leftover money on the card. How many journals can she buy without going over the card’s limit?
Variable: ______________________________
Inequality: ______________________________
Solution: ______________________________
4. Liza wants to have more than $750 in her
savings account before she will leave for college.
Right now she has $300, and she is going to
babysit to earn $12.00 an hour. How many hours
will Liza need to babysit before she leaves for
college?
Variable: ______________________________
Inequality: ______________________________
Solution: ______________________________
5. Dennis is selling chocolate bars for a fundraiser, and if he sells over $175 worth of candy, he’ll win a prize. If chocolates sell for $2.50 a bar, and Dennis has already sold $40 worth of candy, then how many more bars does he have to sell in order to win a prize?
Variable: ______________________________
Inequality: ______________________________
Solution: ______________________________
6. The amusement park won’t allow kids to ride roller-coasters until they are a minimum of 48 inches tall. Michael is now 42 inches tall, and grows about 1/2 inch every month. How many months will it be until Michael can ride a roller-coaster?
Variable: ______________________________
Inequality: ______________________________
Solution: ______________________________
SOLVING INEQUALITIES IN REAL LIFE
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesReview - CCSS
Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.
I CAN SOLVE ONE-STEP INEQUALITIES. 7.EE.4
1.
9p < -81
2.
-2.5d ≥ 30
3.c
2 ≤ −0.75
4.
x – 15 > -20
5.
18 + y ≤ -7
6.
h + 34
< 214
©Maneuvering the Middle LLC, 2016
INEQUALITIES UNIT STUDY GUIDE
I CAN SOLVE TWO-STEP INEQUALITIES. 7.EE.4
7.
-3x – 11 > 45
8.
10 – x ≤ 35
9.x2– 8 ≥ 18
10.
30 < 2x – 6
11.
1.5x + 12 < 18
12.
16 ≥ 6 + x2
I CAN GRAPH INEQUALITY STATEMENTS. 7.EE.4
13. x < 4.5
14.x ≤ -9
15.4
5> x
16.-4.5 < x
17.-9 > x
18.x ≥ 12
I CAN WRITE INEQUALITIES FROM REAL-WORLD PROBLEMS. 7.EE.4
19. Jasmine has a budget of $600.00 to spend on home renovations. She will spend $175.00 on a new sink and the remainder on countertops. The countertops cost $35 per square foot. What is the maximum number of square feet Jasmine can purchase?
Variable: ______________________________
Inequality: ______________________________
20. Hayden earns $9.50 per hour as a lifeguard. He earns a bonus of $50.00 for taking a training course. How many hours must he work to earn at least $300.00?
Variable: ______________________________
Inequality: ______________________________
21. Russell wants to buy three ties and a belt and must spend no more than $80.00. The belt costs $28.50. If the three ties are the same price, then how much can he pay for each tie?
Variable: ______________________________
Inequality: ______________________________
22. An online music service charges a $12.00 registration fee plus $1.50 for each song downloaded. If Mary Beth has a gift card with $60.00, then how many songs can she download?
Variable: ______________________________
Inequality: ______________________________
©Maneuvering the Middle LLC, 2016
I CAN SOLVE REAL-WORLD INEQUALITIES. 7.EE.4
23. Megan is saving up to buy a new cell phone that costs $220.00. So far she has saved $175.00. Megan would like to buy the cell phone in four weeks. Write and solve an inequality to represent at least how much she must save every week to purchase the cell phone.
Inequality: ______________________________
Solution: ______________________________
24. A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will they have less than 100 boxes remaining? Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.
Inequality: ______________________________
Solution: ______________________________
25. A 15-passenger van is rented for a family vacation. The van rental is $60.00 per day, plus a $145.00 insurance fee. How many days can the van be rented if they want to spend no more than $625.00 on the van rental? Write and solve an inequality.
Inequality: ______________________________
Solution: ______________________________
26. Marco is limited to 7 hours of screen time each week. He decides to watch a movie that is 1 hour and 20 minutes on Sunday. If he divides the remainder of the time equally amongst the other six days, then how many minutes can he watch each day? Write and solve an inequality.
Inequality: ______________________________
Solution: ______________________________
I’VE GOT IT!What concepts can I ace on the test?
HELP!What concepts do I need to study?
©Maneuvering the Middle LLC, 2016
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesReview
Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.
I CAN SOLVE ONE-STEP INEQUALITIES.
1.
9p < -81
2.
-2.5d ≥ 30
3.c
2 ≤ −0.75
4.
x – 15 > -20
5.
18 + y ≤ -7
6.
h + 34
< 214
©Maneuvering the Middle LLC, 2016
INEQUALITIES UNIT STUDY GUIDE
I CAN SOLVE TWO-STEP INEQUALITIES.
7.
-3x – 11 > 45
8.
10 – x ≤ 35
9.x2– 8 ≥ 18
10.
30 < 2x – 6
11.
1.5x + 12 < 18
12.
16 ≥ 6 + x2
I CAN GRAPH INEQUALITY STATEMENTS.
13. x < 4.5
14.x ≤ -9
15.4
5> x
16.-4.5 < x
17.-9 > x
18.x ≥ 12
I CAN WRITE INEQUALITIES FROM REAL-WORLD PROBLEMS.
19. Jasmine has a budget of $600.00 to spend on home renovations. She will spend $175.00 on a new sink and the remainder on countertops. The countertops cost $35 per square foot. What is the maximum number of square feet Jasmine can purchase?
Variable: ______________________________
Inequality: ______________________________
20. Hayden earns $9.50 per hour as a lifeguard. He earns a bonus of $50.00 for taking a training course. How many hours must he work to earn at least $300.00?
Variable: ______________________________
Inequality: ______________________________
21. Russell wants to buy three ties and a belt and must spend no more than $80.00. The belt costs $28.50. If the three ties are the same price, then how much can he pay for each tie?
Variable: ______________________________
Inequality: ______________________________
22. An online music service charges a $12.00 registration fee plus $1.50 for each song downloaded. If Mary Beth has a gift card with $60.00, then how many songs can she download?
Variable: ______________________________
Inequality: ______________________________
©Maneuvering the Middle LLC, 2016
I CAN SOLVE REAL-WORLD INEQUALITIES.
23. Megan is saving up to buy a new cell phone that costs $220.00. So far she has saved $175.00. Megan would like to buy the cell phone in four weeks. Write and solve an inequality to represent at least how much she must save every week to purchase the cell phone.
Inequality: ______________________________
Solution: ______________________________
24. A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will they have less than 100 boxes remaining? Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.
Inequality: ______________________________
Solution: ______________________________
25. A 15-passenger van is rented for a family vacation. The van rental is $60.00 per day, plus a $145.00 insurance fee. How many days can the van be rented if they want to spend no more than $625.00 on the van rental? Write and solve an inequality.
Inequality: ______________________________
Solution: ______________________________
26. Marco is limited to 7 hours of screen time each week. He decides to watch a movie that is 1 hour and 20 minutes on Sunday. If he divides the remainder of the time equally amongst the other six days, then how many minutes can he watch each day? Write and solve an inequality.
Inequality: ______________________________
Solution: ______________________________
I’VE GOT IT!What concepts can I ace on the test?
HELP!What concepts do I need to study?
©Maneuvering the Middle LLC, 2016
Name _____________________________________Date ______________________________Pd______
Unit: InequalitiesTest
Solve the inequality problems below. Be sure to show your thinking.
©M
aneuveri
ng t
he M
iddle
LLC
, 2016
1. Solve.
48 > -6x
_____________________
2. Graph.
c ≤ -3
3. Write an inequality to
represent “a number is at
most two”.
_____________________
4. If x = -1, then which of the following
equations makes a true statement?
A. -4x + 9 > 20
B. -4x – 5 < -15
C. -3x + 15 ≤ 18
D. -5x – 15 ≤ -22
5. Which of the following inequalities represents the phrase “three less than twice a number is at least negative one”.
A. 2x + 3 ≥ -1
B. 3 – 2x ≥ -1
C. 3 – 2x ≤ -1
D. 2x - 3 ≥ -1
6. Benny earns $12.00 per hour as a
lifeguard. He earns a bonus of $75.00 for
taking a training course. Which graph best
represents the number of hours must be work
to earn at least $399.00?
A.
B.
C.
D.
7. Xavier needs to bike a minimum of 80
miles this week for his training. If he has
already biked 14 miles this week, then how
many miles should he bike on each of the 6
remaining days this week?
A. x ≥ 12
B. x ≥ 11
C. x ≤ 10
D. x ≥ 10
8. Solve.r
3 – 9 ≥ −2
_____________________
9. Solve. x
8 ≥ −1.5
_____________________
10. Solve.
x – 13 < -11
_____________________
INEQUALITIES UNIT TEST
-5 -4 -3 -2 -1
24 25 26 27 28
24 25 26 27 28
24 25 26 27 28
24 25 26 27 28
Solve the problems below. Be sure to show your thinking.
©M
aneuveri
ng t
he M
iddle
LLC
, 2016
11. Solve.
16 > -8 + x
_____________________
12. Solve.
1.5x + 6 ≤ 31.5
_____________________
13. Solve.
x – 9.5 < -10.5
_____________________
Match the following inequalities to the correct graph below.
14. _____
15. _____
16. _____
17. A fifteen passenger van is rented for a family vacation. The van rental is $75.00 per day, plus a $160.00 insurance fee. Which inequality could be used to find x, the number of days the car be rented if they want to spend less than $760.00 on the van rental?
A. 75.00 + 160.00x < 760.00
B. 75.00x + 160.00 > 760.00
C. 75.00 + 160.00x > 760.00
D. 75.00x + 160.00 < 760.00
18. Emily is encouraged to read more than 4 hours each week. It takes her 45 minutes to finish her first book. She divides the remainder of the time equally amongst the other six days. What is the minimum number of minutes she should read each day?
A. x > 32.5 minutes
B. x > 40 minutes
C. x ≤ 32.5 minutes
D. x ≤ 40 minutes
19. Paulo’s grandfather gave him a collection
of 20 coins. Each month Paulo adds 4 coins
to his collection. Which inequality can be used
to find m, the number of months after starting
his collection when Paulo will have more than
50 coins in his collection?
A. 20m + 4 < 50
B. 20 + 4m < 50
C. 20m + 4 > 50
D. 20 + 4m >50
20. Solve and graph the following inequality.
16 ≥ 6 + x2
Solution: _____________________
Graph:
A. -5 > x
B. x ≤ -3.5
C. -2 < x
D. x > -5
E. -2 > x
F. -3.5 ≤ x
-5 -4 -3 -2 -1
-6 -4 -2 0 2
-5 -4 -3 -2 -1