chapter 6 linear expressions answer key

Chapter 6 – Linear Expressions Answer Key

CK-12 Algebra I Concepts 1

6.1 Inequality Expressions

Answers

1. 𝑥 ≥ 1

2. 𝑥 < −10

3. 𝑥 ≤ −10

4. 𝑥 > 30

5.

6.

7.

8.

9.

10.



6.2 Linear Inequalities

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9. 𝑥 ≤ 2 :



10. 𝑥 > −3

2 :

11. 𝑥 < −25 :

12. 𝑥 ≤ 35 :



6.3 Multi-Step Inequalities

Answers

1. 𝑥 ≥ 3.5

2. 𝑥 < −4

3. 𝑥 ≥ −4

4. 𝑥 ≥ 2

5. 𝑥 ≥11

6

6. 𝑥 > −21

2

7. 𝑥 > 12

8. 𝑥 ≥ −12

5

9. 𝑥 <24

11

10. 𝑥 ≤ −5

11



6.4 Applications with Inequalities

Answers

1. 𝑥 < −3 : (−∞, 3)

2. 𝑥 ≥ 17 : [17, ∞)

3. 𝑥 > −1

12 : (−

1

12, ∞)

4. 𝑥 ≥ −75 : [−75, ∞)

5. 𝑥 >120

31 : (

120

31, ∞)

6. 𝑥 ≥ −7

2 [−

7

2, ∞)

7. 𝑥 > 1 : (1, ∞)

8. −∞ < 𝑥 < ∞ : {−∞, ∞)

9. 𝑥 < −14 : {𝑥 | 𝑥 < −14}

10. 𝑥 ≥ 92 : {𝑥 | 𝑥 ≥ 92}

11. 𝑥 ≥ −15 : {𝑥 | 𝑥 ≥ −15}

12. 𝑥 ≥5

3 : {𝑥 | 𝑥 ≥

5

3}

13. 𝑥 <10

3 : {𝑥 | 𝑥 <

10

3}



14. 𝑥 > −120 : {𝑥 | 𝑥 > −120}

15. 𝑥 > 5 : {𝑥 | 𝑥 > 5}

16. −∞ < 𝑥 < ∞ : {𝑥 | − ∞ < 𝑥 < ∞}

17. {𝑥 | 𝑥 < −1} :

18. {𝑥 | 𝑥 >36

5} :

19. {𝑥 | 𝑥 < −9} :

20. {𝑥 | 𝑥 > −2} :

21. {𝑥 | 𝑥 ≥ −1

5} :

22. {𝑥 | 𝑥 ≥ −11

4} :

23. {𝑥 | 𝑥 < 14} :

24. {𝑥 | 𝑥 ≤ −1

10} :

25. {𝑥 | 𝑥 <3

5} :



26. {𝑥 | 𝑥 ≤3

2} :

27. a. 22.75𝑥 ≤ 71 ∶ 𝑥 ≤ 3.12 : You can attend no more than 3 times

b. Finite

28. 82+95+86+88+𝑥

5≥ 90 : He needs at least a 99 on his 5th test



6.5 Compound Inequalities

Answers

1. −40 ≤ 𝑥 < 60

2. 𝑥 < −2 or 𝑥 ≥ 5

3. −8 < 𝑥 < 0

4. 𝑥 ≤ −2 or 𝑥 > 1.5

5.

6.

7. All real numbers

8.

9.

10.

11.



6.6 Solutions to Compound Inequalities

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.



11. {𝑥 | − 1 ≤ 𝑥 ≤ 17}

12. [−1,17]

13. {𝑥 | 𝑥 <2

3, 𝑥 ≥ 2}

14. No, because there are two value ranges.

a. (−∞,2

3)

b. [2, ∞)

15.

a. [−4

3, −

1

3]

b. [−1,14

5]

c. [−33

8, −

15

4]

d. [−5

2, −1)

16. (−∞, ∞)

17. One

18.

a. Her score must be at least 60, but less than 105

b. Her score must be at least 25, but less than 60.

c. She can’t get an ‘A’ average, based on previous scores.



6.7 Absolute Value

Answers

1. 250

2. 12

3. 0.003

4. 2

5

5. 1

10

6. 23

7. 17

8. 9

9. 5

10. 1.079

11. 113

24



6.8 Absolute Value Equations

Answers

1.

2.

3.

4. No solutions

5.

6.

7.

8.

9.

10.



6.9 Graphs of Absolute Value Equations

Answers

1.

2.

3.



4.

5.

6.



7.

8.

9.

10.



6.10 Absolute Value Inequalities

Answers

1.

2.

3.

4.

5.

6.

7.



8.

9.

10.

11.

12.

13.

a. One: 𝑥 = 0

b. Infinite: −∞ < 𝑥 < ∞

14. 1131

32≤ 𝑥 ≤ 12

31

32

15. 10.5 ≤ 𝑥 ≤ 15.5



6.11 Graphs of Inequalities in One Variable

Answers

1.

2.

3.



4.

5.

6.



7.

8.

9.

10. (All real numbers)



6.12 Linear Inequalities in Two Variables

Answers

1.

2.

3.



4.

5.

6.



7.

8.

9.



10.

a. They have the same slope

b. It is a strip with a slope of 1, running between the two inequalities

11. Translates to the left by 2 units

12. Translates right by 12

13. Reflects across 6x+7=20

14.

15.

a. Zero is not greater than zero

b. It is a false statement

c. Shade to the left (or up)

16.

a. 10𝑥 + 5𝑦 ≥ 2000

b. 10𝑥 + 5𝑦 ≥ 2000 − 1000 − 500 c. 𝑥 + 𝑦 = 100

chapter 6 linear expressions answer key

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