Section 2.4 More on Solving Linear Equations 135 5 6 (x + 12) = PIECE IT TOGETHER 78. Solve: 5 6 (x + 12) = 1 8 (2x - 9) Weston’s work: 1 8 (2x - 9). LCD = 24 24a5 6 (x + 12)b = 24a1 8 (2x - 9)b a24 · 5 6 b (x + 12) = a24 · 1 8 b (2x - 9) 20(x + 12) = 3(2x - 9) 20x + 12 - 6x = 6x - 27 - 6x 14x + 12 - 12=-27 - 12 14x=-39 x=- 39 14 79. Solve: 3x - 5 = 3(x - 5) Katie’s work: 3x - 5 = 3(x - 5) 3x - 5 = 3x - 5 3x - 5 - 3x = 3x - 5 - 3x -5 = -5 Since this is true, the solution is . 80. Solve: -2(x - 1) + x - 3 = x - 1 Mitchell’s work: -2(x - 1) + x - 3 = x -1 -2x + 2 + x - 3 = x - 1 -x - 1 = x - 1 -x - 1 - x = x - 1 - x -2x - 1=-1 -2x - 1 + 1=-1 + 1 -2x = 0 -2x -2 = 0 -2 x = 0 Therefore, the solution is ∅. Calculate It! Solve each equation. Then use a graphing calculator to check the solution. 81. 5x - 1 - (x + 3) = 4x - 4 82. 3x - 4 = 2(x + 1) + x 83. 2 3 (x - 6) = x + 3 84. x 2 + 3 2 = x - x 2 + 3 2 85. 0.86x + 1.25(3.344) = 0.7(x + 11) 86. 0.56x + 0.4(-31.3) = 0.25(x + 2) Think About It! 87. Write an equation that has no solution. 88. Write an equation that has infinitely many solutions. 89. Write an equation that has 0 as a solution. ���������������������������������������������� Determine whether the following is an expression or an equation. (Section 2.1, Objective 1) 1. 2 x - 16 = 0 2. 3 x + 19 Decide if the equation is linear. If the equation is not linear, explain why. (Section 2.2, Objective 1) 3. -x2 + 4 x - 12 = 0 4. 3 2 x - 4 + 5 6 x = 11 Solve each equation. If the equation is a contradiction, write the solution as ∅. If the equation is an identity, write the solution as . (Sections 2.2–2.4 ) 5. y - 5 = 5 6. 8.6 + c = 1.4 7. 2(x - 3) = 3x 8. 9(a - 7) = 4(2a + 3) 9. x 3 = 9 10. -3x + 7 = -14 11. -5.2x + 13.5 = -3.6x + 14.46 12. 3(2z - 6) = 4(z + 5) 13. 2(x - 3) = 3x 14. 5(3a + 1) = 7(2a - 3) 15. 2 3 (x + 6) = 1 2 (x - 4) 16. x + 7 5 - 2 = x - 2 2 17. 0.6x + 4.2 = 0.3(x + 24) 18. x - 2 + 3x = 2(2x - 1) Write an equation that represents each situation. Solve the equation and explain the answer using a complete sentence. (Section 2.3, Objectives 3 and 4 ) 19. The sum of three times a number and 13 is the same as two less than the number. Find the number. 20. The sum of the two smaller of three consecutive odd integers is the same as 82 less than six times the largest integer. Find the integers.
hendricks_beginning_algebra_1e_ch1_3
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