Answer:
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
