110 Chapter 2 Linear Equations and Inequalities For Exercises 9–14, determine whether the given number is a solution to the equation. (See Example 1.) 9. 10. 11. x 1 5; 4 x 2 1; 1 5x 10; 2 3x 21; 7 3x 9 3; 2 2x 1 3; 1 12. 13. 14. Concept 2: Addition and Subtraction Properties of Equality For Exercises 15–34, solve each equation using the addition or subtraction property of equality. Be sure to check your answers. (See Examples 2–3.) 15. x 6 5 16. x 2 10 17. q 14 6 18. w 3 5 19. 20. 21. 22. 2 m 15 6 n 10 23 y 7 9 21 b 23. 24. 25. 26. 4 c 4 13 b 13 4.1 2.8 a 5.1 2.5 y 27. 28. 29. 30. 31. 32. 33. 34. 7 3 x 6.02 c 8.15 p 0.035 1.12 3.245 t 0.0225 1.004 k 3.0589 Concept 3: Multiplication and Division Properties of Equality For Exercises 35–54, solve each equation using the multiplication or division property of equality. Be sure to check your answers. (See Examples 4–7.) 35. 6x 54 36. 2w 8 37. 12 3p 38. 6 2q y 5 39. 5y 0 40. 3k 0 41. 3 42. 3 7 43. 44. 45. 46. 3 10 47. 48. 49. 50. 51. 52. 53. 54. 3.81 0.03p 2.75 0.5q 5.82y 15.132 32.3x 0.4522 Concept 4: Translations For Exercises 55–66, write an algebraic equation to represent each English sentence. (Let x represent the unknown number.) Then solve the equation. (See Example 8.) 55. The sum of negative eight and a number is forty-two. w 41 x 32 y 2 5 1 5 b 4 5 3 8 b 9 2 5 h a 4 4 5 t z 7 1 2 3 x 5 2 1 2 7 p 2 3 5 z 1 2 56. The sum of thirty-one and a number is thirteen. 57. The difference of a number and negative six is eighteen. 58. The sum of negative twelve and a number is negative fifteen. 59. The product of a number and seven is the same as negative sixty-three. 60. The product of negative three and a number is the same as twenty-four. 61. The value 3.2 subtracted from a number is 2.1. 62. The value 3 subtracted from a number is 4.
miller_beginning_intermediate_algebra_4e_ch1_3
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