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180 Chapter 2 Linear Equations and Inequalities in One Variable 79. -5.2 < 1.2x - 2.8 < 5.6 80. 1.5 ≤ 1.8 - 0.3x ≤ 7.5 81. 4(x - 2) -9 ≥ -7x + 16 82. 2(x + 5) - 14 ≤ -9x + 18 83. 3(x - 1) - 5 < 8(x + 2) - x 84. 4(x - 1) + 10 > 9(x + 3) - 2x 85. 2 5 y - 2ay - 3 10 b < 1 2 y + 7 10 86. 3 4 y - 2ay + 1 3 b > 1 2 y - 5 6 87. 12x - 5(2x + 3) > 6(x + 7) - x 88. 16y - 7( y + 4) > 4( y - 2) + y Write an inequality that models each situation. Solve the inequality and answer the question in complete sentences. (See Objective 5.) 89. Mykel scored 85, 78, 72, and 81 on four math tests. What score does she need on the fifth test to have at least an 80 average? 90. Lucas scored 77, 78, and 75 on three math tests. What score does he need on the fourth test to have at least an 80 average? 91. Shanika’s final grade in her math class is based on a weighted average. Homework counts as 5%, quizzes count as 10%, projects count as 10%, tests count as 50%, and the final exam counts as 25%. If she has a homework average of 85, a quiz average of 78, a project average of 90, and a test average of 73, what score does she need on her final exam to have at least an 80 for her final grade? 92. Hassan’s final grade in his math class is based on a weighted average. Homework counts as 10%, quizzes count as 20%, participation counts as 5%, tests count as 40%, and the final exam counts as 25%. If he has a homework average of 88, a quiz average of 82, a participation grade of 100, and a test average of 80, what score does he need on his final exam to have at least an 80 for his final grade? 93. Skype is a software program that allows users to call any number in the world with their computer. Skype offers 12 months of unlimited phone calls in the United States for $29.95 per year. Sergeant Walker is stationed in Iraq for one year. Skype charges 37.2¢ per minute plus 3.9¢ per international call. If Sergeant Walker’s family calls him once a week for the year, the cost of the phone service is given by C = 29.95 + 0.372m + 0.039(52) = 31.978 + 0.372m where m is the number of minutes. How many minutes can the family talk in a year so that their cost in phone calls for the year is at most $1000? (Source: http://www.skype.com) 94. The cost to rent a car for a week from a luxury rental agency is $350 plus 44 cents per mile. How many miles can be driven if you have at most $500 to rent the car for a week? Round to the nearest whole number. Mix ’Em Up! Solve each inequality. Graph the solution set and write the solution set in interval notation and in set-builder notation. 95. -x + 12 < -12 96. -y + 16 ≥ 14 97. 9x - 20 > -2 98. -10y + 19 ≤ 39 99. 0.2a - 7 ≤ -1.5 100. -0.32b + 4 < 10.4 101. y 8 - 2 ≤ 6 102. - 1 3 x + 5 > 4 3 103. - 5 8 x - 3 ≤ 3 8 104. 1 4 y + 3 ≥ 11 4 105. -11 < 2a - 1 < 17 106. 15 < 6b - 3 ≤ 21 107. -5 ≤ 4x + 3 ≤ 19 108. 2 ≤ 5 - 3y < 26 109. -9 < -2a + 5 < 5 110. -6 ≤ 4b + 10 < 2 111. 12 - 2(x - 3) > -2x + 1 112. 6x - (3x - 2) > 3x + 1 113. 7x + 2(x + 5) < 9x + 8 114. x - (4x - 2) > 5 - 3x 115. 5 2 x + 3ax + 3 2 b ≥ 9 2 x - 7 2 116. 8 3 y - 2ay - 2 11 b ≥ 5 3 y - 2 11 117. -7 ≤ -3(x - 3) + 2 ≤ -1 118. -3 < -2(y + 4) + 7 < 5 119. - 7 2 < 1 3 x - 1 < 13 6 120. - 4 5 ≤ 1 2 y + 2 ≤ 11 5 121. -3.8 < 0.25x - 2.8 < 13.2 122. 2.5 ≤ 0.12y + 3.1 < 12.7 Write an inequality that models each situation. Solve the inequality and answer the question in complete sentences. 123. Azziz scored 57, 97, and 85 on three math tests. What score does he need on the fourth test to have at least an 80 average? 124. Elaine scored 84, 60, and 63 on three chemistry tests. What score does she need on the fourth test to have at least an 70 average? 125. Derek’s final grade in his math class is based on a weighted average. Homework counts as 10%, quizzes count as 20%, tests count as 50%, and the final exam counts as 20%. If he has a homework average of 67,


hendricks_beginning_algebra_1e_ch1_3
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