146 Chapter 2 Linear Equations and Inequalities in One Variable Solve each linear equation and check your answer. If there is no solution, then write for your answer. (Section 2.1, Objectives 4 and 5) 50. 12 + 4x = 4(1 - x) 51. 5x 3 - 3x 2 = 1 6 52. 5(x + 3) - 4x = x - 5 Solve the linear equation and check your answer. If there is no solution, then write for your answer. (Section 2.1, Objectives 4 and 6) 53. 6(x - 2) - 5x = x - 12 54. 8(2x + 1) - 6x = x - 10 55. 7(x - 4) - x = 6(x - 5) + 2 Translate each problem into a linear equation and solve the problem. (Section 2.2, Objective 1) 56. The product of a number and one-third is 60. Find the number. 57. The quotient of a number and four is eight. Find the number. 58. Five greater than three times a number yields 17. Find the number. 59. Twice the sum of two consecutive odd numbers is 88. Find the numbers. Find the measure of each unknown angle. (Section 2.3, Objective 1) 60. Find the measure of an angle whose complement is 15° more than twice the measure of the angle. 61. Find the measure of an angle whose supplement is 33° less than twice the measure of the angle. 62. 3a – 10 a – 4 63. 8x – 9 5x + 6 64. Find the height of a triangle whose area is 108 ft2 and whose base is 9 ft. 65. The length of a rectangle is 2 ft less than three times its width. If the perimeter is 280 ft, find the length and width of the rectangle. Solve each formula for the specified variable. (Section 2.3, Objective 4) 66. a = 2 5 b - cd for b 67. x = 1 2 y + 3zw for z Graph the solution set of each inequality on a number line and express the solution set in interval notation and set-builder notation. (Section 2.4, Objective 1) 68. 3 < x 69. -10 ≥ x Solve each inequality. Graph the solution set and write your answer in interval notation and set-builder notation. (Section 2.4, Objective 2) 70. -24 ≤ -6a 71. 2 3 (x + 3)<-x + 5 The following students are taking algebra from Professor Fowser. In Professor Fowser’s class, the course grade is determined by tests (40%), homework (10%), quizzes (20%), and a final exam (30%). Answer each student’s question. (Section 2.4, Objective 3) 72. Paulos: This semester, my test average is 85, homework average is 100, and quiz average is 65. What do I have to get on the final exam to earn a B in the class, if a B is 80–89? 73. Jennifer: My test average is 74, and my homework average is 85, and my quiz average is 63. I just want to earn a C in the class, so what do I have to get on the final exam, if a C is 70–79? Find the intersection and union of the sets. Write the solution in interval notation. (Section 2.5, Objectives 1 and 2) 74. A = -13, -1, B = -12, -1 75. A = 4, 20, B = (4, 20) Solve each compound inequality. Write the solution in interval notation. (Section 2.5, Objective 3) 76. x > 7 and x > 5 77. x ≤ -3 and x ≤ -7 Solve each compound inequality. Write the solution in interval notation. (Section 2.5, Objective 4) 78. x ≥ 10 or x ≥ 15 79. 5x + 3 > 8 or 7x - 4 ≤ -3 Solve each equation. (Section 2.6, Objectives 1 and 2) 80. |5 - x| = 12 81. |8 - 2x| = |3x + 6| 82. |3x + 6| = 0 83. |16 - 2x| = 0 Solve each problem. (Section 2.6, Objective 3) 84. Suppose a digital scale reflects a weight (in pounds) with an absolute error of 0.4 lb. If someone weighs 184.3 lb according to the scale, find the possible values for the exact weight of the person. 85. Suppose a countertop food scale reflects a weight (in ounces) with an absolute error of 0.1 oz. If a piece of chicken weighs 3 oz according to the scale, find the possible values for the exact weight of the piece of chicken.
hendricks_intermediate_algebra_1e_ch1_3
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