Section 2.1 Solving Linear Equations 63 SECTION 2.1 EXERCISE SET Write About It! Use complete sentences in your answer to each exercise. 1. What is a linear equation? 2. What does it mean for an equation to be conditional? Give an example. 3. What does it mean for an equation to be a contradiction? Give an example. 4. What does it mean for an equation to be an identity? Give an example. 5. Explain why the addition property of equality covers subtraction. 6. Explain why the multiplication property of equality covers division. 7. How can you determine if a linear equation is a contradiction? 8. How can you determine if a linear equation is an identity? Practice Makes Perfect! Determine if each equation is a linear equation. If it is a linear equation, determine if -1 is a solution of the equation. (See Objective 1.) 9. 5x + 1=-4 10. 2x + 7 = 5 11. 4x - 3 = 7 12. 6x - 5=-1 13. 3x - 2 5 =-1 14. 4x + 3 4 = 3 15. 2m2 + 3 = 5 16. 5m2 - 6=-1 17. 2(x - 1) + 3 = 4 18. 5(x - 2) + 1 = 3 19. 1 - 3x = 2(x + 3) 20. 5 - 4x = 3(x - 1) 10x2 + 5x - 1 21. x = 7 22. 6x2 - 10x + 4 x = 12 Use the addition property of equality to solve each linear equation and check the answer. (See Objective 2.) 23. x + 1 2 =3 24. x + 1 3 = 1 25. y - 1 = 1 4 26. y - 4 = 2 3 27. 3x + 9 3 =2 28. 4x + 8 4 = 3 29. 6x - 12 6 = 10 30. 5x - 15 5 = 9 31. 6.5 = a + 14.5 32. 12.3 = a + 10.3 33. 14 = x - 23 34. 10 = x - 11 35. 16 - d = 13.5 36. 19 - d = 12.2 37. 5 - d = 6.5 38. 7 - d = 14.9 Use the multiplication property of equality to solve each linear equation and check the answer. (See Objective 3.) 39. x 3 =-2 40. x 6 =-5 41. a 11 =6 42. a 9 = 12 43. 3x - 8 4 =4 44. 4x - 9 3 = 2 45. 2y - 7 7 =1 46. 5y - 8 8 = 2 47. 6x + 13 =9 48. 4x - 9 = 11 49. 2x - 6 =7 50. 3x - 10 = 5 51. 1 - 2x =9 52. 2 - 3x = 8 53. 10 - 4g =2 54. 9 - 5g = 4 Solve each linear equation and check the answer. If there is no solution, then write for the answer. (See Objectives 4 and 5.) 55. 6x - 7x + 1 = 4 - x 56. 2x - 3x - 5 = 5 - x 57. 5x + 3 = 5(1 + x) 58. 7x - 2 = 7(3 + x) 59. 2(1 - 3a) = 4(a - 1) 60. 3(4 - 2 a) = 5(a + 3) 61. 9 - 3x = 3(x - 7) 62. 12 - 4x = 4(x + 1) 4x - 12 63. 2 = 3x + 6 64. 15x - 20 5 = 2x + 4 65. 5(2y - 1) = 4 - (6y + 2) 66. 6(3y - 4) = 7 - (10y - 5) 67. 4m 3 - 1 2 = 5 2 68. 5m 2 - 1 3 = 2 3 69. 3m 2 - 1 4 =- 5 4 70. 3m 5 - 1 5 =- 2 5 71. 5x 3 - 3x 2 = 1 6 72. 7x 4 - x 2 = 5 8
hendricks_intermediate_algebra_1e_ch1_3
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