409 3.6 Polynomial and Rational Inequalities Solve each rational inequality. Give the solution set in interval notation. See Examples 4 and 5. 49. (a) x - 1 x - 2 Ú 0 (c) x - 1 x - 2 … 0 (b) x - 1 x - 2 70 (d) x - 1 x - 2 60 50. (a) 3x 2x - 5 Ú 0 (c) 3x 2x - 5 … 0 (b) 3x 2x - 5 70 (d) 3x 2x - 5 60 51. x x - 3 … 0 52. x x - 5 … 0 53. x - 1 x - 4 70 54. x + 1 x - 5 70 55. 2x + 3 x - 5 … 0 56. 3x + 7 x - 3 … 0 57. 8 x - 2 Ú 2 58. 20 x - 1 Ú 1 59. x - 8 x - 4 63 60. 2x - 3 x + 1 74 61. x2 - 3x - 4 x2 + 6x + 9 … 0 62. x2 - x - 2 x2 - 2x + 1 Ú 0 63. 1 x + 2 7 1 x - 3 64. 1 x - 1 6 1 x + 1 65. 2 x - 2 Ú 1 x 66. 5 x + 3 Ú 3 x 67. 3 4 - x 7 6 1 - x 68. 5 2 - x 7 3 3 - x 69. 1 x2 - 4 … 1 2 - x 70. 1 x2 - 4x + 3 … 1 3 - x Concept Check Write a rational inequality for each of the given solution sets. 73. (a) 1-4, 32 (b) 1-4, 34 (c) 1-∞, -42 ´13, ∞2 (d) 1-∞, -42 ´33, ∞2 74. (a) 1-2, 12 (b) 3-2, 12 (c) 1-∞, -22 ´11, ∞2 (d) 1-∞, -24 ´11, ∞2 71. (a) 1-5, 12 (b) 3-5, 14 (c) 1-∞, -52 ´11, ∞2 (d) 1-∞, -54 ´31, ∞2 72. (a) 1-1, 02 ´11, ∞2 (b) 3-1, 04 ´31, ∞2 (c) 1-∞, -14 ´30, 14 (d) 1-∞, -12 ´10, 12 Concept Check Write a polynomial inequality for each of the given solution sets. (Modeling) Solve each problem. Write the answers using an inequality. 75. The $64,000 Question If $1000 is invested at an interest rate of x hundred percent for 3 yr compounded annually, the balance in dollars is given by the function ƒ1x2 = 10001x3 + 3x2 + 3x + 12. For what values of x will the balance exceed $64,000? 76. Stopping Distance Under certain conditions, the number of feet a car will skid after the brakes are fully applied is given by the function d1x2 = 0.05x2 + x, x 70, where x is the speed of the car in miles per hour. For what values of x will the car skid at most 120 ft?
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