Unit 5 Inequalities - quipsd.org

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


-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.


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


8x + 10 > 6x – 20 x > -15


3(x + 6) + 2x < 5x + 12 Empty Set


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


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


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


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


Example 4: x > 3 or x > 7 x > 3


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


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


186

Review Question What is the difference between and and or?

And – both things 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


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



187




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)




188




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


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


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.


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



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


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


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


Solve.

1. | x | = 7

2. | x | < 2

3. | x | > 5



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


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


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



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


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


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)


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


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


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



198

15. 5x + 2y < 9 16. 4x – y > 6

17. y < -3 18. y + x > 3

19. y > x 20. y > 2x – 1

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


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


Example 3: Graph: 323

1 xy

Why can’t we see the line? Not in the proper window


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



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


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.

206

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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Standardized Test Review

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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?

Unit 5 Inequalities - quipsd.org

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