114 Chapter 2 Linear Equations and Inequalities in One Variable 55. 12x≤-60 or 7 - 9x > 3 56. 13x ≥ 65 or 11 - 5x > 6 57. 5x + 3 > 8 or 7x - 4≤-3 58. 2x + 5 > 6 or 3x - 1≤-4 59. 5x + 1 ≤ 7 or 6x - 2 < 1 60. 4x - 7 < 9 or 2x + 3 < 4 61. 10(2 - 9x) ≥ 20 or 2(1 + 3x) > 6 62. 10(3 - x) ≤ 15 or 3(2 - 5x) > 13 Write a compound inequality that represents each situation and solve the inequality. Use a complete sentence to answer each question. (See Objective 5.) 63. If Lawrence’s quiz scores are 90, 82, 75, and 78, what must he earn on his fifth quiz to have an average between 80 and 89? 64. If Emma’s quiz scores are 99, 89, 80, and 70, what must she earn on her fifth quiz to have an average between 80 and 89? 65. Sakinah’s course grade is based on a weighted average. The weights are as follows: homework (15%), quizzes (25%), tests (40%), and final exam (20%). If Sakinah’s homework average is 100, quiz average is 90, and test average is 86, what must she score on the final exam to have an average between 90 and 100? 66. Su Ming’s course grade is based on a weighted average. The weights are as follows: homework (15%), quizzes (25%), tests (40%), and final exam (20%). If Su Ming’s homework average is 75, quiz average is 70, test average is 83, what must she score on the final exam for her course average to be between 80 and 89? 67. A cell phone company charges a monthly fee of $29.99 for 300 anytime cell phone minutes and $0.40 per additional minute. How many additional minutes can a subscriber use if he budgets between $40 and $50 for his phone bill? 68. A cell phone company charges a monthly fee of $49.99 for 800 anytime cell phone minutes and $0.25 per additional minute. If Callie budgets a range of $70 to $100 each month for her phone bill, how many additional minutes can she afford to use? 69. Miguel pays $3000 to rent a hall for his fiftieth birthday party. The buffet costs $18 per person. If Miguel has between $4000 and $5000 to spend on his party, how many people can he invite to his birthday party? 70. Marianne is planning a graduation party for her daughter. She finds a banquet hall that charges $850 and a caterer who charges $20 per person. If Marianne can spend between $2000 and $3000 on the party, how many people can attend the party? Mix ’Em Up! Solve each problem. Write each answer in interval notation when applicable. 71. -7, 8 ∪ (-3, 12) 72. (-20, 5) ∪ -5, 9 73. -20, 9 (-20, 9 74. -1, 2 (-1, 2 75. (-∞, 6 ∪ (6, ∞) 76. (-∞, 3) ∪ 3, ∞) 77. (-∞, 3) (6, ∞) 78. (-∞, 5 10, ∞) 79. (-∞, 6.5) ∪ -3.5, 12.2) 80. (-∞, 6.5) -3.5, 12.2) 81. 2, 7 82. (-9, 7) 83. ∪ (-10, ∞) 84. ∪ -1, ∞) 85. 7x + 6 < 11 or 5x - 5 > 12 86. 10x - 5 ≥ 2 and 4x + 3 < 10 87. 2(1 - 4x) > 10 and 4x - 5 < 11 88. 3(2 - x)>-6 and 6x + 1 < 7 89. 2 3 x - 7 6 > 5 6 or 3 5 x + 1 2 < 7 10 90. 3 4 x - 1 8 > 1 or 5 6 x + 2 < 2 3 91. 1 - 3 7 x < 1 2 and 1 + 1 2 x < 3 5 92. 2 - 5 2 x > 13 2 and 7 3 x - 1 > 2 5 93. 3 - 4x ≤ 0 or 6x + 1 > 3 94. 2 - 5x ≤ 1 or 4x - 3 > 5 95. 8x + 9 > 3 and 7x - 2>-3
hendricks_intermediate_algebra_1e_ch1_3
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