Section 2.4 Linear Inequalities and Applications 99 72. In what year will the total national health expenditures for the Department of Veterans’ Affairs exceed $60 billion? Mix ’Em Up! Solve each inequality. Graph the solution set and write it in interval notation and set-builder notation. 73. 13<-5a 74. 8≥-4a 75. 5 + 2(3 - x) < 5(x - 2) 76. 12 - 3(x - 4) ≥ 6(x + 1) 77. 4(2x - 1) ≥ 9x + 1 78. 5(3x + 4) < 20x - 10 79. 1.3 + 0.2(8 - x) < 0.7(2x - 5) 80. 3.5 - 0.3(6 + x) > 0.8(7 - 2x) 81. 6y - 9 < 14y + 3 82. 3y + 2 < 10y - 6 83. 64≥-8x 84. -54>-18x 85. 1 2 (3x - 6) ≥ 2(x - 4) 86. 2 3 (6x + 3) > 4(3x - 5) 87. 4(8 - 7x) < 6(1 + 3x) 88. -4(1 - 6x) ≥ 2(4x - 3) 89. 0.36(5x - 3) ≤ 0.6(7 - x) 90. 0.25(8x - 6) ≥ 1.8(1 - 5x) 91. Hope’s history course grade is based on a weighted average. The weights are as follows: tests (50%), term paper (30%), and final exam (20%). If Hope’s test average is 80 and she scores 89 on her term paper, what must she score on the final exam to maintain at least an 80 course average? 92. Fiona’s English course grade is based on a weighted average. The weights are as follows: midterm (30%), papers (45%), and final exam (25%). If Fiona earns 70 on her midterm and 75 on her papers, what must she score on her final exam to maintain at least a 70 course average? 93. Mandy rents a small reception hall for her wedding for $500. She hires a caterer who charges $25 per person. If she has $2500 to spend on her reception and caterer, how many people can she have at her reception? 94. Bette rents a banquet hall for her wedding reception for $5000 and they provide dinner at $40 per person. If Bette’s budget is $15,000, how many people can she have at her reception? The following students are taking algebra from Dr. Cheng. In Dr. Cheng’s class, the course grade is determined by tests (55%), quizzes (20%), and a fi nal exam (25%). Answer each student’s question. 95. Jada: My test average is 76, and my quiz average is 71. I need to earn a B in the class to keep my 3.0 GPA. If an 80–89 is a B, what do I need to earn on the final exam to earn at least B in the class? 96. Fredericka: My test average is 95 and my quiz average is 85. What do I have to get on the final exam to earn an A in the class, if 90–100 is an A? The total of all Low Income Home Energy Assistance Program (LIHEAP) funds allocated to states, in billions of dollars can be approximated by the equation L = 1.19x + 3.017, where x is the number of years after 2008. (Source: http://www.acf.hhs.gov) 97. In what year will the total of all LIHEAP funds exceed $6.5 billion? 98. In what year will the total of all LIHEAP funds exceed $9 billion? You Be the Teacher! Correct each student’s errors, if any. 99. 2x + 5 ≥ 8x - 7 Ada’s work: 2x + 5 ≥ 8x - 7 12 ≥ 6x x ≥ 1 2 a1 2 , ∞b e x` x ≥ 1 2 f 100. 1 3 (2x + 10)≤-2 (x - 1) Wanda’s work: 1 3 (2x + 10)≤-2 (x - 1) 2x + 10≤-6x - 1 8x≤-11 x≥- 11 8 c- 11 8 , ∞b e x` x≥- 11 8 f
hendricks_intermediate_algebra_1e_ch1_3
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