96 Chapter 1 Linear Equations and Inequalities in One Variable Mixed Exercises For Exercises 65–74, solve the compound inequality. Write the answer in interval notation. 65. a. 66. a. and 3x 5 6 19 and 2x 3 6 23 0.516x 82 7 0.8x 7 41x 12 6 7.2 3x 5 6 19 or 2x 3 6 23 0.516x 82 7 0.8x 7 or 41x 12 6 7.2 b. b. 8x 4 6.4 or 0.31x 62 2r 4 8 or 3r 5 8 0.6 67. a. 68. a. 8x 4 6.4 and 0.31x 62 2r 4 8 and 3r 5 8 0.6 b. b. 2 4x 69. 70. 1 6 3 x 2 3 6 8 4 0 3 7 1w 32 5 41t 32 4w 3t 71. or 72. or 6 6 12t 814 t2 5 31w 52 6w y 7 3 6 1 4 1 x 4 7 2 x 3 x 3 4 x 5 73. or 74. or y 1 2 7 2 7 Concept 5: Applications of Compound Inequalities 75. The normal number of white blood cells for human blood is between 4800 and 10,800 cells per cubic millimeter, inclusive. Let x represent the number of white blood cells per cubic millimeter. (See Example 11.) a. Write an inequality representing the normal range of white blood cells per cubic millimeter. b. Write a compound inequality representing abnormal levels of white blood cells per cubic millimeter. 1 3 76. Normal hemoglobin levels in human blood for adult males are between 13 and 16 grams per deciliter (g/dL), inclusive. Let x represent the level of hemoglobin measured in grams per deciliter. a. Write an inequality representing normal hemoglobin levels for adult males. b. Write a compound inequality representing abnormal levels of hemoglobin for adult males. 77. A polling company estimates that a certain candidate running for office will receive between 44% and 48% of the votes. Let x represent the percentage of votes for this candidate. a. Write a strict inequality representing the expected percentage of votes for this candidate. b. Write a compound inequality representing the percentage of votes that would fall outside the polling company’s prediction. 78. A machine is calibrated to cut a piece of wood between 2.4 in. thick and 2.6 in. thick. Let x represent the thickness of the wood after it is cut. a. Write a strict inequality representing the expected range of thickness of the wood after it has been cut. b. Write a compound inequality representing the thickness of wood that would fall outside the normal range for this machine. 79. Twice a number is between and 12. Find all such numbers. (See Example 12.) 3 80. The difference of a number and 6 is between 0 and 8. Find all such numbers. 81. One plus twice a number is either greater than 5 or less than 1. Find all such numbers. 82. One-third of a number is either less than 2 or greater than 5. Find all such numbers.
miller_intermediate_algebra_4e_ch1_3
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