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Page One:

21. D

22. B

Page Two:

12. B

13. D

14. C

15. A

Page 3:

10. C

11. D

Page 4:

7. B

8. B

9. C

Page 5:

5. D

6. D

Step-by-step explanation:

Question 21:

Absolute values are always greater or equal to zero.

Question 22:

Same as question 21.

Page 2 Below

Question 12:

Apply absolute rule:

x + 1 = -10 or x + 1 = 10

Solve for x (subtract 1 from each side):

x + 1 = -10

x = -11

Solve for x in the other equation (subtract 1 from each side):

x + 1 = 10

x = 9

Question 13:

Subtract 3 from both sides:

3 - 7 l -1 + 2x l - 3 = -116 - 3

Simplify:

-7 l -1 + 2x l = -119

Divide both sides by -7 and simplify:

l -1 + 2x l = 17

Apply absolute rule:

-1 + 2x = -17

-1 + 2x = 17

Solve (Subtract -1 from both sides):

2x = -16

x = -8

Solve (Add 1 to both sides):

2x = 18

x = 9

Question 14:

Subtract 8 from both sides:

8 - l 2n - 8 l - 8 = 0 - 8

Simplify:

- l 2n - 8 l = -8

Divide both sides by -1 and simplify:

l 2n - 8 l = 8

Apply absolute rule:

2n - 8 = -8

2n - 8 = 8

Solve (Add 8 to both sides):

2n = 0

n = 0

Solve (Add 8 to both sides):

2n = 16

n = 8

Question 15:

Apply absolute rule:

r - 2 < -2

r - 2 > 2

Therefore:

r < 0

r > 4

Page 3 below

Question 10:

Intervals (Solve):

9x - 1 > 9 - x

= x > 1

7x - 4 ≥ 4 + 9x

= x ≤ -4

Combine and/or merge intervals:

x ≤ -4 or x > 1

Question 11:

Solving 7 + 4x < 4x - 7 yields no solution.

However, -x + 6 > x + 6 does.

Combine and/or merge intervals and solve:

x < 0

Page 4 below:

Question 7:

If a ≤ u ≤ b then a ≤ u and u ≤ b:

-69 ≤ 6x - 9 and 6x - 9 ≤ -45

Intervals (Solve):

: x ≥ -10

: x ≤ -6

Combine and/or merge intervals:

-10 ≤ x ≤ -6

Question 8:

If a ≤ u ≤ b then a ≤ u and u ≤ b:

-93 ≤ 9n - 3 and 9n - 3 < -84

Intervals:

n ≥ -10

n < -9

Combine and/or merge intervals:

-10 ≤ n < -9

Question 9:

4k - 6 ≤ -6 + 6k or -3k - 5 ≥ -2k + 10

Intervals:

: k ≥ 0

: k ≤ -15

Merge and/or combine intervals:

k ≤ -15 or k ≥ 0

Page 5 below

Question 5:

2 - 3n < 17

6n + 4 < 58

Intervals:

n > -5

n < 9

Combine and/or merge intervals:

-5 < n < 9

Question 6:

6x + 5 > -49 and 7 - 4x ≥ -21

Intervals:

: x > -9

: x ≤ 7

Combine and/or merge intervals:

-9 < x ≤ 7

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step-by-step explanation: