SECTION A.9 Interval Notation; Solving Inequalities A85 Applications and Extensions In Problems 109–118, find a and b. 109. If x 1 1, − < < then a x b 4 . < + < 110. If x 3 2, − < < then a x b 6 . < − < 111. If x 2 3, < < then a x b 4 . <− < 112. If x 4 0, − < < then a x b 1 2 . < < 113. If x 0 4, < < then a x b 2 3 . < + < 114. If x 3 3, − < < then a x b 1 2 . < − < 115. If x 3 0, − < < then a x b 1 4 . < + < 116. If x 2 4, < < then a x b 1 6 . < − < 117. If x 6 3 12, < < then a x b. 2 < < 118. If x 0 2 6, < < then a x b. 2 < < 119. What is the domain of the variable in the expression x3 6? + 120. What is the domain of the variable in the expression x 8 2 ? + 121. A young adult may be defined as someone older than 21 but less than 30 years of age. Express this statement using inequalities. 122. Middle-aged may be defined as being 40 or more and less than 60. Express this statement using inequalities. 123. Life Expectancy The Social Security Administration determined that an average 30-year-old man in 2023 could expect to live at least 52.2 more years and that an average 30-year-old woman in 2023 could expect to live at least 55.8 more years. (a) To what age could an average 30-year-old man expect to live? Express your answer as an inequality. (b) To what age could an average 30-year-old woman expect to live? Express your answer as an inequality. (c) Who can expect to live longer, a male or a female? By how many years? Source: Social Security Administration, 2023 JAN 2023 ? ? 55. If x 0 5 , < < then < < 0 1 1 . 56. If x 4 0, ≤− < then ≤ < 1 1 0. 57. If x 5 0, − < < then < < 1 1 0. 58. If x 0 10, < ≤ then < ≤ 0 1 1 . In Problems 59–108, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 59. x 1 5 + < 60. x 6 1 − < 61. x 3 5 7 − ≤− 62. x 2 3 5 − ≤ 63. x3 7 2 − > 64. x2 5 1 + > 65. x x 3 1 3 − ≥ + 66. x x 2 2 3 − ≥ + 67. x 2 3 8 ( ) − + < 68. x 3 1 12 ( ) − − < 69. x 4 3 1 3 ( ) − − ≤ 70. x x 8 4 2 2 ( ) − − ≤− 71. x x 1 2 4 8 ( ) − > + 72. x x 3 4 1 3 2 ( ) + > − 73. x x 2 1 4 ≥ − 74. x x 3 2 6 ≥ + 75. x 0 3 7 5 < − ≤ 76. x 4 2 2 10 ≤ + ≤ 77. x 5 4 3 2 − ≤ − ≤ 78. x 3 3 2 9 − ≤ − ≤ 79. x 3 2 1 4 0 − < − < 80. x 0 3 2 2 4 < + < 81. x 1 1 1 2 4 < − < 82. x 0 1 1 3 1 < − < 83. x x x x 2 3 1 1 ( )( ) ( )( ) + − > − + 84. x x x x 1 1 3 4 ( )( ) ( )( ) − + > − + 85. x x x 4 3 2 1 2 ( ) ( ) + ≤ + 86. x x x 9 5 3 1 2 ( ) ( ) − ≤ − 87. x 1 2 1 3 3 4 ≤ + < 88. x 1 3 1 2 2 3 < + ≤ 89. x4 2 0 1 ( ) + < − 90. x2 1 0 1 ( ) − > − 91. x 1 4 7 1 ( ) − ≥ − 92. x 2 3 5 3 1 ( ) + ≤− − 93. x 0 2 3 5 < < 94. x 0 4 2 3 < < 95. x 0 2 4 1 2 1 ( ) < − < − 96. x 0 3 6 1 3 1 ( ) < + < − 97. x2 8 < 98. x3 12 < 99. x3 12 > 100. x2 6 > 101. x2 1 1 − ≤ 102. x2 5 7 + ≤ 103. x 1 2 3 − > 104. x 2 3 1 − > 105. x4 5 9 − + − ≤ 106. x 4 2 − − ≤ 107. x2 4 − ≥ − 108. x 2 1 − − ≥
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