Post on 04-Dec-2021
177
Unit 5 – Inequalities
5–1 One/Two Step Inequalities
5–2 Multi-Step Inequalities
5–3 Compound Inequalities
5–4 Absolute Value Inequalities
5–5 Graphing Two Variable Inequalities
178
Review Question
What four things make up an equation? Numbers, variables, operations, and equal sign
Discussion What makes an equation, an equation? Equal sign
What makes an inequality, an inequality? Inequality
> greater than
≥ greater than or equal to
< less than
≤ less than or equal to
What is the answer to x + 4 = 9? There is one solution. It is 5. Look at the solution on a number line.
What is the answer to x + 4 > 9? Anything bigger than 5. There is an infinite amount of solutions.
Look at the solution on a number line.
As far as we know, an equation has one solution. An inequality has an infinite number of solutions.
SWBAT solve a multi-step inequality
Definitions > greater than
≥ greater than or equal to
< less than
≤ less than or equal to
Example 1: Solve. Then graph your solution.
2x + 2 > 6 x > 2
Example 2: Solve. Then graph your solution.
-4x + 5 ≤ 25 x > -5
Why is our answer wrong? Didn’t flip the inequality
Rule: Flip the inequality when you multiply or divide by a negative number.
Example 3: Solve. Then graph your solution.
423
x
x > -18
Why don’t we flip the inequality? We are not multiplying by a negative
Section 5-1: One/Two Step Inequalities (Day 1)
179
You Try!
Solve. Then graph your solution.
1. 2x – 6 < 8 x < 7
2. -3x – 7 > 14 x < -7
3. 232
x
x > -10
4. 243
x x > 6
5. 2x – 4 > -12 x > -4
6. 104
43
x x < -12
What did we learn today?
Solve each inequality. Then graph your solution.
1. 3x > 12 4 2. 54
x 20 3. -5z < 20 -4
4. 43
x
-12 5. y – 6 > 7 13 6. z + 1 < 8 7
7. 5x + 3 > 23 4 8. 3x – 14 < 4 6 9. -3y – 5 > 19 -8
10. 5x + 6 < -29 -7 11. 8 – 5y > -37 9 12. 18 – 4y > 42 -6
13. .4y – 3 < -1 5 14. 3.2x + 2.6 > -23 -8 15. 843
x
12
16. 852
x -6 17. 4
3
3
x 9 18. -5y + 10 < -15 5
19. 874
3x 20 20. 5 + 4y > 25 5 21. 2x + 8 < -8 -8
Section 5-1 Homework (Day 1)
180
Review Question
When do you flip the inequality sign? When you multiply/divide by a negative number
Discussion We solved more complicated equations like this:
3(4x + 2) = 10x – 20
Today, we will do the same with inequalities.
SWBAT solve a multi-step inequality
Example 1: Solve. Then graph your solution.
8x + 10 > 6x – 20 x > -15
Example 2: Solve. Then graph your solution.
3(x + 6) + 2x < 5x + 12 Empty Set
Example 3: Solve. Then graph your solution.
8x – (2x + 4) < 4x + 10 x < 7
You Try! Solve. Then graph your solution.
1. 4x + 12 > 2x + 24 x > 6
2. 15x < 5(2x + 10) x < 10
3. 2x – (x – 5) > 2x + 17 x < -12
4. 3(2x + 2) > 6x – 4 0 > 10
5. 8x + 4 > 2(x + 6) + 6x Empty Set
6. x > 3
What did we learn today?
Section 5-2: Multi Step Inequalities (Day 1)
333
128
x
x
181
Solve. Then graph the solution.
1. 4x + 10 > 2x + 20 5 2. 6x + 4 < 3x + 13 3
3. 3x – 5 < 7x – 21 4 4. 3x + 10 < -11 -7
5. 3 – 4x > 10x + 10 -1/2 6. 2(3y + 1) < 6 + 6y All Reals
7. 4(x – 2) > 4x Empty Set 8. 6(x + 2) – 4 > -10 -3
9. 4(2y – 1) > -10(y – 5) 3 10. 3(1 + y) < 3y + 3 All Reals
11. 2(x – 3) + 5 > 3(x – 1) 2 12. 6x + 7 > 8x – 13 10
13. 8y + 9 > 7y + 6 -3 14. 2x + 8 > 20 6
15. 5.3 + 2.8x > 4.9x + 1.1 2 16. -5x + 15 < 10 1
17. 5x – 9 > -3x + 7 2 18. -3(2n – 5) > 4n + 8 7/10
19. 2(2x + 3) + 4x > 7x + 4 -2 20. 852
x
-26
Section 5-2 Homework (Day 1)
182
Review Question
Let’s take a look at problem #10 on last night’s homework. When we solve it we get 0 < 0. When is this
true?
It says “When is 0 less than or equal to 0”. The key word is “or”. It only has to be one or the other
(less than OR equal to). Zero is always less than OR equal to zero. This will help us during the
next section.
Discussion We wrote equations like: Two more than twice a number is equal to twenty less than 3n.
2n + 2 = 3n – 20
Today, we will write inequalities.
SWBAT write and solve a multi-step inequality
Example 1: Write and inequality. Then solve. Then graph your solution.
Eight less than four times a number is greater than six more than twice number.
4n – 8 > 2n + 6; n > 7
Example 2: Write and inequality. Then solve. Then graph your solution.
Three times the quantity of 2n + 9 is less than or equal to 11 decreased by twice a number.
3(2n + 9) < 11 – 2n; n < -2
What did we learn today?
Solve. Then graph the solution.
1. 8x + 2 > 2x + 20 3 2. 6x + 4 + 4x < 24 2
3. 2x – 8 < 7x – 38 6 4. -4x + 10 < -18 7
5. 5 – 8x > 10x + 23 -1 6. -4(3y + 1) < 6 – 12y All Reals
7. -(x + 5) > -x Empty Set 8. 2(x + 2) – 4 > -8 -4
9. 4(3y – 1) > -10(y – 5) 27/11 10. -3x + 8 > 8 0
Section 5-2: Multi Step Inequalities (Day 2)
Section 5-2 In-Class Assignment (Day 2)
183
Write an inequality. Then solve.
11. A number decreased by 5 is less than 22. 27
12. Seven times a number is greater than 28. 4
13. An integer increased by 10 is at least 20. 10
14. Negative four times a number is at most 20. -5
15. Four times a number plus ten is less than or equal to two times a number decreased by twenty. -15
16. Negative 8x plus five is greater than seven less than 4x. 1
17. Four times the quantity of 3n + 5 is less than or equal to 10n – 8. n < -14
18. The quotient of a number and 5 increased by 2 is greater than -10. -60
184
Review Question When do you flip the inequality sign? When you multiply/divide by a negative number
Discussion Today’s lesson involves understanding the words and, and or.
So let’s try a real life example first.
I’m in my house and at school. When? Never
I’m in my house or at school. When? When I’m at one place or the other.
SWBAT solve a compound inequality.
Definitions And – both things must be true
Or – at least one thing must be true
Example 1: x < 3 and x > -5 -5 < x < 3
(Use dry erase boards as a visual. Have two students hold dry erase boards in the front of the class.
One student will put a ‘3’ on their board with an arrow pointing left. The other student will have ‘-
5’ on their board with an arrow pointing right. Have the students visualize the where both thing
are happening.)
Example 2: x < 3 or x > -5 All Reals
(use dry erase boards as a visual)
Example 3: x > 3 and x > 7 x > 7
(use dry erase boards as a visual)
Example 4: x > 3 or x > 7 x > 3
(use dry erase boards as a visual)
You Try! Solve.
1. x > 4 and x < -2 Empty Set
2. x > 4 or x < -2 x > 4 or x < -2
3. x > 3 and x > 4 x > 4
4. x > 3 or x > 4 x > 3
What did we learn today?
Section 5-3: Compound Inequalities (Day 1)
185
Solve each compound inequality.
1. x > 3 and x < 12
2. x > -5 or x > -3
3. x < -1 and x < -10
4. x > 5 or x < -8
5. x > -5 and x < -11
6. x > -5 or x < 5
7. x > -8 and x < 8
8. x > 5 and x < 8
9. x < -3 and x < -6
10. x > 3 or x > -5
Section 5-3 Homework (Day 1)
186
Review Question What is the difference between and and or?
And – both things must be true
Or – at least one thing must be true
Let’s make sure we know what we are doing:
x > -2 and x < 5 -2 < x < 5
Discussion Today, we are going to combine the idea of and and or with our solving skills.
2x + 5 > 11 or 3x – 5 < 10
We will solve the inequalities first. Then figure out the correct solution set.
SWBAT solve a compound inequality
Definitions And – both things must be true
Or – at least one thing must be true
Example 1: 3x + 8 < 2 or x + 12 > 2 – x x < -2 or x > -5
Example 2: 3 < -2x + 7 and 2x + 7 < 15 x < 2
You Try! Solve.
1. 3x + 5 < -7 or -4x + 8 < 20 x < -4 or x > -3
2. -1 < x + 3 < 5 -4 < x < 2
3. 2(x – 4) < 3x + 6 and x – 8 < 4 – x -14 < x < 6
4. 2x – 8 + 3x < 7 or 3(2x + 4) > 30 All Reals
What did we learn today?
Section 5-3: Compound Inequalities (Day 2)
187
Review Question What is the difference between and and or?
And – both things must be true
Or – at least one thing must be true
Discussion Let’s make sure we know what we are doing by going over some homework problems.
How do we get better at something? Practice
Today will be a day of practice.
SWBAT solve a compound inequality
Example 1: 3x + 8 > 8 or 3x + 14 > 2 – x x > -3
Example 2: 5x + 7 < 27 and -3x – 5 > -8 x < 1
Solve each compound inequality.
1. x > 3 and x < 8 2. x > 5 or x > -2
3. x < -3 and x > 5 4. x > -2 or x < 1
5. x > 3 and x > 5 6. x > 3 or x < -3
7. x > 5 or x < 5 8. x > -3 and x < -3
9. x + 3 < 7 or x – 6 > 8 10. 2x + 6 < 12 and -4x + 10 < -22
11. 3x + 2 > 5 or 6 + 3x < 2x + 7 12. 42
3
x or 53
2
x
13. -3x + 5 < 20 or 652
x 14. 2(3x – 3) > 5 and 2x + 4x – 5 > 2x + 15
15. 3(x + 1) + 11 < -2(x + 13) and 3x + 2(4x + 2) < 2(6x + 1)
What did we learn today?
Section 5-3: Compound Inequalities (Day 3)
Section 5-3 In-Class Assignment (Day 3)
188
Review Question What is the difference between and and or?
And – both things must be true
Or – at least one thing must be true
Discussion What does absolute value mean? The distance something is from zero.
Notice that distance is always positive. For example, if you travel to Florida it is not a negative distance
because you went south. You can see this on a map. Going south or west on a map does not represent a
negative distance. So: | 3 | = ? | -3 | = ?
SWBAT solve an inequality with an absolute value
Example 1: This is a difficult topic so try some easy ones first:
|x| = 3 When is x’s distance from zero equal to ‘3’? When ‘x’ is 3 or -3
|x| > 3 When is x’s distance from zero greater than ‘3’? When x > 3 or x < -3
|x| < 3 When is x’s distance from zero less than ‘3’? When x < 3 and x > -3; -3 < x < 3
Example 2:
|x| = 7.2 When is x’s distance from zero equal to ‘7.2’? When ‘x’ is 7.2 or 7.2
|x| > 7.2 When is x’s distance from zero greater than ‘7.2’? When x > 7.2 or x < 7.2
|x| < 7.2 When is x’s distance from zero less than ‘7.2’? When x < 7.2 and x > 7.2; -7.2 < x < 7.2
You Try! 1. |x| = 2 x = 2 or -2
2. |x| < 6 -6 < x < 6
3. |x| > 4.2 x > 4.2 or x < 4.2
4. |x| > 7 x > 7 or x < -7
5. |x| < 1 -1 < x < 1
What did we learn today?
Section 5-4: Absolute Value Inequalities (Day 1)
189
Solve each inequality.
1. | x | = 5
2. | x | < 3
3. | x | > 1
4. | x | < 6
5. | x | > 10
6. | x | > 2
7. | x | < 9
8. | x | > 10
9. | x | < 4.5
10. | x | > 4
1
Section 5-4 Homework (Day 1)
190
Review Question What does absolute value mean? The distance something is from zero.
Notice that distance is always positive.
Discussion You always want to make absolute statements. So:
Is a > problem always ‘or’ ? No.
Is a < problem always ‘and’ ? No.
SWBAT solve an inequality with an absolute value
Example 1: |x| > -5 When is x’s distance from zero greater than ‘-5’? Always. > problems are not always ‘or’
|x| < -5 When is x’s distance from zero less than ‘-5’? Never. < problems are not always ‘and’
Example 2: |x| > 0 When is x’s distance from zero greater than ‘0’? When x > 0 or x < 0; Everything except
‘0’
|x| < 0 When is x’s distance from zero less than or equal to ‘0’? When x = 0; Think of not going
on vacation. How far did you travel? 0 miles
* > problems are not always ‘or’; < problems are not always ‘and’
You Try! 1. |x| = 4 x = 4 or -4
2. |x| < 8 -8 < x < 8
3. |x| > -2 All Reals
4. |x| < 0 Empty Set
5. |x| < 5.2 -5.2 < x < 5.2
6. |x| < -6 Empty Set
What did we learn today?
Section 5-4: Absolute Value Inequalities (Day 2)
191
Solve each inequality.
1. | x | = 7
2. | x | < 6
3. | x | > -1
4. | x | < 3
5. | x | > 0
6. | x | > 4.2
7. | x | < -9
8. | x | > 1
9. | x | < 2.5
10. | x | > 3
1
Section 5-4 Homework (Day 2)
192
Review Question Let’s make sure we understand some easy ones first:
|x| = 2 x = 2 or -2
|x| > 2 x > 2 or x < -2
|x| < 2 -2 < x < 2
Discussion What would | pen | > 3 mean?
The distance that the pen is from zero is the following: pen > 3 or pen < -3
SWBAT solve an inequality with an absolute value
Example 1: |x – 3| = 5
x – 3 = 5 or x – 3 = -5
x = 8 x = -2
Example 2: |2x + 3| < 11
2x + 3 < 11 and 2x + 3 > -11
x < 4 and x > -7
-7 < x < 4
Example 3: |2x + 3| > 11
2x + 3 > 11 or 2x + 3 < -11
x > 4 or x < -7
You Try! 1. |5x – 5 | = 15 4, -2
2. |2x + 4| < 6 -5 < x < 1
3. |2x + 4| > 10 x > 3 or x < -7
4. |4x + 2| < -7 Empty Set
5. |-x + 2| < 4 -2 < x < 6
6. |6x + 2| > -6 All Reals
What did we learn today?
Solve.
1. | x | = 7
2. | x | < 2
3. | x | > 5
Section 5-4: Absolute Value Inequalities (Day 3)
Section 5-4 Homework (Day 3)
193
4. | x | > -3
5. | x | < -2
6. | x – 5 | = 8
7. | x + 9 | = 2
8. | 2x – 3 | = 17
9. | 5x – 8 | = 12
10. | x – 2 | < 5
11. | x + 8 | < 2
12. | x + 3 | > 1
13. | x – 6 | > 3
14. | 3x + 2 | > -7
15. | 2x + 4 | > 8
16. | 2x + 1 | < 9
17. | 6x + 8 | < -1
18. | -x + 3 | > 1
194
Review Question What would | pen | < 3 mean?
The distance that the pen is from zero is the following: -3 < pen < 3
Discussion Why can’t we always assume that a “>” problem is an “or”?
Can you give an example of a “>” problem that isn’t an “or”?
|x + 3| > -4; All Real Numbers
SWBAT solve an inequality with an absolute value
You Try! 1. |5x + 10 | = 5 -1, -3
2. |2x + 5| < 9 -7< x < 2
3. |x + 8| > 1 x > -7 or x < -9
4. |2x – 3| > -2 All Reals
5. |-x + 5| < 4 1 < x < 9
6. |2x – 4| < 0 x = 2
What did we learn today?
Solve.
1. | x | = 5 2. | x | < 6
3. | x | > 1 4. | x | > -5
5. | x | < -8 6. |x| < 0
7. | x – 4 | = 8 8. | x + 8 | = 2
9. | 2x – 4 | = 12 10. | 5x – 5 | = 20
11. | x – 5 | < 5 12. | x + 5 | < 2
13. | 2x + 4 | > 8 14. | -2x – 6 | > 3
15. | 2x + 2 | > -7 16. | 6x + 8 | < -1
Section 5-4: Absolute Value Inequalities (Day 4)
Section 5-4 In-Class Assignment (Day 4)
195
Review Question What does absolute value mean? The distance something is from zero.
Discussion How would you graph y = 2x + 3? Start at (0, 3), up 2 over 1
How would you graph y < 2x + 3? Start at (0, 3), up 2 over 1. Then determine which side should be
shaded.
SWBAT graph an inequality with two variables
Example 1: Graph: y < 2x + 3 Start at (0, 3), up 2 over 1
Should the line be dotted or solid? Solid
Example 2: Graph: y + 4x < -2 Start at (0, -2), down 4 over 1
Should the line be dotted or solid? Dotted
Example 3: Graph: y > -2 Horizontal line at -2
Should the line be dotted or solid? Dotted
Hmmmm?!? What would be our test point for y > x? Anything but (0, 0)
You Try! Graph each inequality.
1. y > -2x + 4 Start at (0, 4), down 2 over 1
2. y – 4x < -3 Start at (0, -3), up 4 over 1
3. 3x – y > -1 Start at (0, 1), up 3 over 1
4. y > 2x Start at (0, 0), up 2 over 1
5. 4x + 2y > 8 Start at (0, 4), down 2 over 1
6. x < 2 Vertical line at 2
What did we learn today?
Graph each inequality.
1. y > 2x + 3 2. y < -3x + 2
3. y < -x – 3 4. y > 4x – 4
5. y + 2x > 1 6. -y > 4x + 3
7. y > 3x 8. y > 2
Section 5-5: Graphing Two Variable Inequalities (Day 1)
Section 5-5 Homework (Day 1)
196
9. 2y + 3x > 4 10. x < 3
11. y < -2x 12. y > 5x – 2
13. y + 3x > -2 14. x > -3
15. 4x + 3y < 8 16. 3x – y > 5
17. y < -1 18. y + x > 1
19. y > 5x 20. y > 3x – 8
197
Review Question How do you know which side of the line to shade? Use a test point
Why is (0,0) usually a good test point? It is easy and it doesn’t intersect most lines
When would (0, 0) not be a good test point? When the line goes through the origin
Discussion How do we get better at something? Practice
Today will be a day of practice.
SWBAT graph an inequality with two variables
Example 1: Graph: y < -3x + 1 Start at (0, 1), down 3 over 1
Should the line be dotted or solid? Solid
You Try! Graph.
1. y > 2x + 1 Start at (0, 1), up 2 over 1 2. y + x < 3 Start at (0, 3), down 1 over 1
3. 2x – y > 1 Start at (0, -1), up 2 over 1 4. y > x Start at (0, 0), up 1 over 1
5. 6x + 3y > 8 Start at (0, 8/3), down 2 over 1 6. y < 5 Horizontal line at 5
What did we learn today?
Graph each inequality.
1. y > 4x + 1 2. y < -2x + 6
3. -y < 2x – 3 4. y > -6x – 4
5. y + 2x > 1 6. -y > 4x + 3
7. 3y + 6 > 3x 8. x > 5
9. 2y + 3x > 4 10. x < -1
11. y < 2x – 10 12. y > 5x
13. y – 3x > -1 14. y > -7
Section 5-5: Graphing Two Variable Inequalities (Day 2)
Section 5-5 In-Class Assignment (Day 2)
199
This lesson uses graphing calculators. This lesson can be done without them and used
as another day of practice.
Review Question How do you know if the line should be dotted or solid? > or >
Discussion Today we will be using the calculator to graph some inequalities.
Why do you think that I let you use the calculator?
you will be using them in the future, give more precise answers, easier, use them on standardized
tests
SWBAT graph an inequality with two variables using a graphing calculator
Example 1: Graph: y < -4x + 5 Start at (0, 5), down 4 over 1
Should the line be dotted or solid? Solid
Example 2: Graph: 5y – 2x < 3 Start at (0, 3/5), up 2 over 5
What issue do we have putting this inequality into the calculator? Must be in “y =” form
Should the line be dotted or solid? Dotted
Example 3: Graph: 323
1 xy
Why can’t we see the line? Not in the proper window
What did we learn today?
Graph each of the inequalities by hand.
1. y > -4x + 5 2. -y < 2x – 3 3. y + 4x > -1
4. 4y + 6 > 3x 5. x > 5 6. y > 4x
7. 43
2 xy 8. y > 2.5 9. y < 3x + 30
Section 5-5: Graphing Two Variable Inequalities (Day 3)
Section 5-5 In-Class Assignment (Day 3)
200
Graph each of the inequalities using the graphing calculator.
10. y > -3x + 5 11. 42
1 xy 12. y > x
13. y – 3x > -1 14. y > -4 15. y < 10x + 50
15. 5x + 2y < 9 16. 4x – y > 6 18. x > 10
201
Review Question How do you know which side of the line to shade? Test point
Why is (0,0) usually a good test point? The line usual doesn’t intersect it.
When wouldn’t (0,0) be a good test point? When it goes through (0, 0)
SWBAT review for the Unit 5 Test
Discussion 1. How do you study for a test? The students either flip through their notebooks at home or do not
study at all. So today we are going to study in class.
2. How should you study for a test? The students should start by listing the topics.
3. What topics are on the test? List them on the board
- Solving inequalities
- Compound inequalities
- Inequalities with absolute values
- Graphing inequalities
4. How could you study these topics? Do practice problems
Practice Problems
Have the students do the following problems. They can do them on the dry erase boards or as an
assignment. Have students place dry erase boards on the chalk trough. Have one of the groups explain
their solution.
Solve.
1. 72
103
x 2. 84
3
x
3. 5(x + 2) > 2(3 – x) 4. x > 3 or x < -3
5. y < 2 and y > -5 6. 3y – 8 > -14 and -2y – 8 > 4
7. |x| > 11 8. |x| < 4
9. |2x + 7| > 5 10. |-3x – 5| < 8
11. |5x| > -5 12. |-x + 2| < -1
Unit 5 Review
202
Graph each inequality on the coordinate plane.
13. 5x > 15
14. y > 5x – 7
15. 2x + 3y < -12
What did we learn today?
203
SWBAT do a cumulative review
Discussion What does cumulative mean?
All of the material up to this point.
Does anyone remember what the first five chapters were about? Let’s figure it out together.
1. Pre-Algebra
2. Solving Linear Equations
3. Functions
4. Linear Equations
5. Inequalities
Things to Remember:
1. Reinforce test taking strategies: guess/check, eliminate possibilities, work backwards, and estimating.
2. Reinforce the importance of retaining information from previous units.
3. Reinforce connections being made among units.
1. What set of numbers does .25 belong?
a. counting b. whole c. integers d. rationals
2. 4 x 2 = 2 x 4 is an example of what property?
a. Commutative b. Associative c. Distributive d. Identity
3. What is the value of 8 – 12 ?
a. -20 b. 20 c. 4 d. -4
4. What is the value of (3.5)(-24) ?
a. -84 b. -8.4 c. -.84 d. -85
5. What is the value of -11.5 ÷ 2.5 ?
a. -4.6 b. -.46 c. -.046 d. -64
6. What is the value of 9
2
6
12 ?
a. 17/18 b. 16/18 c. 43/18 d. 35/18
In-Class Assignment
UNIT 5 CUMULATIVE REVIEW
204
7. What is the value of 4
3
2
19 ?
a. 35/3 b. 38/3 c. 1/2 d. 12/3
8. 43
a. 4 b. 8 c. 12 d. 64
9. 529=
a. 17 b. 23 c. 27 d. 264.5
10. 200 =
a. 100 b. 210 c. 10 d. 102
11. 18 – (9 + 3) + 22
a. 10 b. 28 c. 32 d. 2
12. 3x + 4y – 8x + 6y
a. 11x +10y b. 5x + 2y c. 5x + 10y d. -5x + 10y
13. 2x + 8 = 14
a. 11 b. -11 c. 3 d. -3
14. 2(x – 3) – 5x = 4 – 5x
a. 5 b. 6 c. Empty Set d. Reals
15. 3(x + 4) + 2x = 12 + 5x
a. 5 b. 6 c. Empty Set d. Reals
16. Solve for y: 3a + 2y = -5x
a. y = 5x – 3a b. 2
35 axy
c. y = -5x – 3a d. y = -5x – 3a/2
17. Solve for y; given a domain of {-2, 0, 5} for y = 2x + 4.
a. -2, 4, 5 b. 0, 4, 14 c. 0, 4, 8 d. 0, 14, 15
18. If f(x) = 4x – 2, find f(2).
a. 3 b. 4 c. 6 d. 10
205
19. Which equation is not a linear equation?
a. -4x + y = 3 b. yx
4 c. x = 2 d. 32 xy
20. Which equation is not a function?
a. 73 xy b. 5y c. x =-5 d. 22
1 xy
21. Write an equation of a line that passes through the points (2, 5) and (7, 20).
a. y = -3x + 6 b. y = 3x – 11 c. y = 3x – 1 d. y = 3x + 1
22. Write an equation of a line that passes through the point (-3, 2) and has a m = 3.
a. y = -3x – 2 b. y = 3x + 11 c. y = -3x + 7 d. y = -3x – 7
23. Write an equation of a line that has m = -2 and a y-intercept of -7.
a. y = 2x – 7 b. y = -2x + 7 c. y = -2x – 7 d. y = -2x
24. Write an equation of a line that is perpendicular to 22
1 xy and passes through the point (-2, 4).
a. y = -2x + 8 b. y = -2x + 8 c. y = -2x d. y = -2x – 11
25. Write an equation of a line that is parallel to y – 3x = -5 and passes through the point (5, -3).
a. y = 3x – 18 b. y = 3x + 12 c. y = -3x + 18 d. y = 3x – 11
26. Which of the following is a graph of: y = -2x – 5?
a. b. c. d.
27. Which of the following is a graph of: x = 3?
a. b. c. d.
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28. What is the y-intercept of the line y = 4x + 12?
a. 12 b. 3 c. -3 d. 9
29. What is the x-intercept of the line y = 4x + 12?
a. 9 b. 3 c. -3 d. 12
30. 1262
x
a. x < -36 b. x < 36 c. x > 36 d. x > -36
31. x > -3 and x > 2
a. -3 < x < 2 b. x > -3 c. 3 < x < -2 d. x > 2
32. |4x – 2| < 10
a. x < 3 or x > -2 b. x > 3 and x < -2 c. -2 < x < 3 d. x < 3
33. |2x + 8| > 14
a. x > 3 or x < -11 b. x > 3 and x < -11 c. x < -11 d. x > 3
34. |4x + 1 | > -2
a. x > -3/4 b. x < 1/2 c. Empty Set d. All Reals
35. Which of the following is a graph of: y > 2x + 3.
a. b. c. d.
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1. Which inequality describes the set of points graphed below?
a. x < -2 b. x < -2 c. x > 2 d. x > 2
2. The solution set of an inequality is graphed on the number line below. The graph shows the solution
set of which inequality?
a. 2x + 5 < -1 b. 2x + 5 < -1 c. 2x + 5 > -1 d. 2x + 5 > -1
3. The graph shown below is the graph of which inequality?
a. 0 < p < 3 b. p > 0 or p < 3 c. p < 0 or p < 3 d. 0 < p < 3
4. Solve: |x – 6| > 14
a. -8 < x < 20 b. x > 20 or x > -8 c. x > 20 or x < -8 d. 2 < x < 12
5. A baseball team had $1000 to spend on supplies. The team spent $185 on a new bat. New baseballs
cost $4 each. The inequality 185 + 4b < 1000 can be used to determine the number of new baseballs (b)
that the team can purchase. Which statement about the number of new baseballs that can be purchased is
true?
a. The minimum number of baseballs that can be purchased is 185.
b. The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.
c. The maximum number of baseballs that can be purchased is 185.
d. The team can purchase 204 baseballs.
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6. The following problem requires a detailed explanation of the solution. This should include all
calculations and explanations.
a. Graph the following inequality: y > -4x + 2
b. How do you know if the line is solid or dotted?
c. How do you know which side of the line to shade in?
d. Which test point should you use when graphing y > x?