Equations with Variables on Both Sides ALGEBRA 1 LESSON 2-4 pages 98–101  Exercises 1. 9 2. 7 3. 3 4. 5 5. 7 6. 3 7. 3 8. –2 9. 7 10. –3 11. –3 21. a. Answers may vary. Sample: 0 :  9 = 9 3 :  –9 = –9 –4 :  33 = 33 –6 :  45 = 45 b. identity 22. identity 23. no solution 24. identity 25. identity 26. no solution 27. no solution 28. no solution 12. 3 13. 2 14. 5 15. 4 16. 5 17. 16.95 + 0.05m = 22.95 + 0.02m; 200 min 18. 44 + 30m = 99 + 25m; 11 months 19. 4b – 3 = 3b + 5; 8 ft 20. 100 + 80h = 250 + 70h; 15 h 2-4

Equations with Variables on Both Sides ALGEBRA 1 LESSON 2-4 29. 0 30. identity 31. 10 32. no solution 33. no solution 34. –2 35. 0 36. identity 37. – 38. 1500 + 8t = 12t; 375 teddy bears 39. 1200 + 9b = 25b; 75 bags 40. x = –1, a = – , w = –4, y = 0 41. a = 3, b = 5, c = 7, d = 11 42. x = 5, w = 3, y = 2, a = 9 43. a = 3, b = 6, c = 5, d = 44. The student forgot a negative sign on the left side of the equation; –5. 45. The student subtracted y from both sides instead of adding y to both sides; 5.3. 46. DE = 10, DF = 7, EF = 6 1 4 47. No; an equation with a solution of 0 has a solution. An equation with no solution is not true for any value of the variable. 48. a. no b. 1 and 3; at 3, 4 – 3(x + 1) is greater than 5(x – 3), while at 1 the opposite is true. The values must be the same for x between 1 and 3. c. for values of x greater than 2 1 3 1 5 2 3 2-4

Equations with Variables on Both Sides ALGEBRA 1 LESSON 2-4 49. Answers may vary. Sample: 3x = 12x 50. Answers may vary. Sample: 4x + 4 = 3x + 7 51. Answers may vary. Sample: – + 4 = 2x + 7 52. Answers may vary. Sample: 3x + 1 = 3(x + ) 53. Answers may vary. Sample: 14x – 12 = 7(2x + 3) 54. Answers may vary. Sample: 7x – 2 = 5x 55. 18 units 56. rectangle: 6 units, 2 units, 4 units, 4 units 57. D 58. G 59. C 60. H 61. C 62. I 63. A 64. 7 65. –4 66. 1.68 67. –6 68. 20.84 69. 1 70. 4 in. 71. – , – , – 72. 5.009, 5.04, 5.043 73. 8.02, 8.1, 8.3 74. –100, –87, 93, 500 75. –1.24, 0.45, 1.23, 2.24 76. –9.8, 0.9, 8.6, 9.7 1 4 4 5 5 8 3 5 x 2 1 3 2 3 2-4