College Algebra Essentials 2nd Edition Blitzer Solutions Manual

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50.

6( x − 1) − (4 − x) ≥ 7 x − 8 6x − 6 − 4 + x ≥ 7x − 8

58.

7 x − 10 ≥ 7 x − 8 −10 ≥ −8 Not true for any x.

The solution set is the empty set, ∅.

60. |x| < 5 –5 < x < 5 The solution set is { x − 5 < x < 5} or (–5, 5).

52. 7 < x + 5 < 11 7 – 5 < x + 5 – 5 < 11 – 5 2<x<6 The solution set is { x 2 < x < 6} or (2, 6).

61. |x – 1| ≤ 2 –2 ≤ x – 1 ≤ 2 –1 ≤ x ≤ 3 The solution set is { x − 1 ≤ x ≤ 3} , or [–1, 3].

53. –3 ≤ x – 2 < 1 –1 ≤ x < 3 The solution set is { x − 1 ≤ x < 3} , or [–1, 3).

62. |x + 3| ≤ 4 –4 ≤ x + 3 ≤ 4 –7 ≤ x ≤ 1 The solution set is { x −7 ≤ x ≤ 1} or [–7, 1].

54. –6 < x – 4 ≤ 1 –2 < x ≤ 5 The solution set is {x | −2 < x ≤ 5} or (–2, 5].

63. |2x – 6| < 8 –8 < 2x – 6 < 8 –2 < 2x < 14 –1 < x < 7 The solution set is { x − 1 < x < 7} , or (–1, 7).

55. –11 < 2x –1 ≤ –5 –10 < 2x ≤ –4 –5 < x ≤ –2 The solution set is { x − 5 < x ≤ −2} , or (–5, –2].

64.

56. 3 ≤ 4x – 3 < 19 6 ≤ 4x < 22 6 22 ≤x< 4 4 3 11 ≤x< 2 2

3x + 5 < 17

–17 < 3x + 5 < 17 –22 < 3x < 12 22 ⎧ ⎫ The solution set is ⎨ x − < x < 4 ⎬ or 3 ⎩ ⎭ ⎛ 22 ⎞ ⎜ − , 4⎟ . ⎝ 3 ⎠

⎧ 3 11 ⎫ ⎡ 3 11 ⎞ The solution set is ⎨ x ≤ x < ⎬ or ⎢ , ⎟ .

2 2 ⎣2 2 ⎠ ⎩ ⎭ −3 ≤

1 x − 4 < −3 2 1 −2 ≤ x < 1 2 −4 ≤ x < 2 The solution set is { x − 4 ≥ x < 2} or [ −4, 2 ) . −6 ≤

59. |x| < 3 –3 < x < 3 The solution set is { x − 3 < x < 3} , or (–3, 3).

51. 6 < x + 3 < 8 6–3<x+3–3<8–3 3<x<5 The solution set is { x 3 < x < 5} , or (3, 5).

57.

Chapter 1 Review Exercises

65. |2(x – 1) + 4| ≤ 8 –8 ≤ 2(x – 1) + 4 ≤ 8 –8 ≤ 2x – 2 + 4 ≤ 8 –8 ≤ 2x + 2 ≤ 8 –10 ≤ 2x ≤ 6 –5 ≤ x ≤ 3 The solution set is { x − 5 ≤ x ≤ 3} , or

2 x − 5 < −1 3

2 x<4 3 3≤x<6 The solution set is { x 3 ≤ x < 6} , or [3, 6).

2≤

[–5, 3].

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