698
Appendix B
21. |9x| − 11 = x
22. 2x − 7 = |x + 1|
Case 1:
Case 2: −9x − 11 = x −10x = 11 x = −11/10
9x − 11 = x 8x = 11 x = 11/8
x + 5 =6 23. 2 − x
Case 1: 2x − 7 = x + 1 x= 8
x − 3 =5 24. x + 4
Case 1: Case 2: x+5 x+5 = −6 =6 2−x 2−x x + 5 = 12 − 6x x + 5 = −12 + 6x 7x = 7 −5x = −17 x= 1 x = 17/5 25.
|x + 6| < 3 −3 < x + 6 < 3
Case 1: Case 2: x−3 x−3 =5 = −5 x+4 x+4 x − 3 = 5x + 20 x − 3 = −5x − 20 −4x = 23 6x = −17 x = −23/4 x = −17/6 26.
−9 < x < −3 S = (−9, −3)
27.
|2x − 3| ≤ 6 −6 ≤ 2x − 3 ≤ 6 −3 ≤ 2x ≤ 9 −3/2 ≤ x ≤ 9/2 S = [−3/2, 9/2]
Case 1:
Case 2: x + 2> 1 x + 2 < −1 x > −1 x < −3 S = (−∞, −3) ∪ (−1, +∞)
31. |5 − 2x| ≥ 4 5 − 2x ≥ 4 −2x ≥ −1
|7 − x| ≤ 5 −5 ≤ 7 − x ≤ 5 −12 ≤ −x ≤ −2 12 ≥ x ≥ 2 S = [2, 12]
28.
|3x + 1| < 4 −4 < 3x + 1 < 4 −5 < 3x < 3 −5/3 < x < 1 S = (−5/3, 1)
1 30. x − 1 ≥ 2 2
29. |x + 2| > 1
Case 1:
Case 2: 2x − 7 = −(x + 1) 3x = 6 x = 2; not a solution because x must also satisfy x < −1
Case 2: Case 1: 1 1 x − 1≥ 2 x − 1 ≤ −2 2 2 1 1 x≥ 3 x ≤ −1 2 2 x≥ 6 x ≤ −2 S = (−∞, −2] ∪ [6, +∞) 32. |7x + 1| > 3
Case 2: 5 − 2x ≤ −4 −2x ≤ −9
x ≤ 1/2 x ≥ 9/2 S = (−∞, 1/2] ∪ [9/2, +∞)
Case 1: 7x + 1 > 3 7x > 2
Case 2: 7x + 1 < −3 7x < −4
x > 2/7 x < −4/7 S = (−∞, −4/7) ∪ (2/7, +∞)