Section 2.5 Compound Inequalities 115 96. 7x - 1 ≥ 5 and 3x + 4>-2 97. 3x - 5 > 7 or 2x + 6 < 1 98. 12x - 4 ≤ 8 and 3x + 2 > 2 99. 0.3x + 0.12 < 3.27 and 0.4x - 1.36 > 0.54 100. 1.56x - 3.2 ≥ 2.26 and 0.8x + 5.6 ≤ 2.4 101. 2x + 6 < 8 or 4x - 9 < 2 102. 8x - 3 ≤ 3 or 5x - 1 < 7 Write a compound inequality that represents each situation and solve the inequality. Use a complete sentence to answer each question. 103. Frederick needs the work of an electrician. He finds an electrician that charges $50 to make a service call plus $30 per hour. If Frederick plans to spend between $110 and $500, how many hours can he afford to hire the electrician? 104. Roberto hires a professional organizer to organize his home office. The professional organizer charges a flat fee of $75 plus $25 per hour. If Roberto budgets between $600 and $800 to get his office organized, how many hours can he afford to hire the professional organizer? 105. Maddy wants to maintain a test average between an 80 and 89. If Maddy’s test scores are 85, 96, 89, and 78, what must she score on her fifth test? 106. Isaac wants to maintain a quiz average between 70 and 79. If Isaac’s quiz scores are 84, 69, 73, 81, and 70, what must he score on his sixth quiz? You Be the Teacher! Answer each student’s question. 107. Jacquesha: On a test, my answer to a question was {0}. My teacher marked it wrong and said that the answer was the empty set. What is the difference between {0} and ? 108. Lori: I do not understand the exercises that require me to fi nd the intersection of the empty set and another set. Please explain how to do this type of problem. Correct each student’s errors, if any. 109. Solve 10 - 3x < 4 and 5x + 23 > 3. Josh’s work: 10 - 3x < 4 and 5x + 23 > 3 -3x<-6 and 5x>-20 x < 2 and x>-4 The solution set is (-4, 2). 110. Solve 28 - 4x > 4 or 28 - 4x<-4. Mark’s work: 28 - 4x > 4 or 28 - 4x<-4 -4x>-24 or -4x<-32 x > 6 or x < 8 The solution set is (-∞, ∞). Calculate It! Solve each compound inequality and use a graphing calculator to confi rm each solution. 111. 6x + 7 > 1 and 5x - 2 < 13 112. 3x - 2 > 10 and 4x - 5 < 23 113. 5x - 7 ≤ 33 or 7x > 14 114. 2x ≥ 18 or 3x - 4 < 23
hendricks_intermediate_algebra_1e_ch1_3
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