Answer Key – Chapter 7

Exercise 7.1

1. 1. [latex]2x - 3[/latex]
   2. [latex]\displaystyle{\frac{2x}{5}}[/latex]
   3. [latex]25 + 3x[/latex]

3. 1. i. 3   ii. 0   iii. 3, 7, –4
   2. i. 2   ii. 0   iii. 1, –5
   3. i. 4   ii. 2   iii. 9, 7, –6

5. 1. i. 3   ii. 5   iii. 5, –3
   2. i. 3   ii. 1   iii. –2, 3
   3. i. 3   ii. 7   iii.–2, –2

7. 1. [latex]12A[/latex] and [latex]-7A[/latex]; [latex]4B[/latex] and [latex]-B[/latex]
   2. [latex]6x[/latex] and [latex]-5x[/latex]; [latex]8y[/latex] and [latex]-3y[/latex]

9. 1. [latex]-2x, 5x[/latex] and [latex]-12x[/latex]; [latex]8[/latex] and [latex]-3[/latex]
   2. [latex]6xy^2[/latex] and [latex]2xy^2[/latex]; [latex]-2x^2y[/latex] and [latex]3x^2y[/latex]; [latex]-4x^2[/latex] and [latex]2x^2[/latex]

11. 24

13. 65

15. 1. [latex]\displaystyle{\frac{23}{9}}[/latex]
    2. 24

17. 1. 30
    2. 22

Exercise 7.2

1. 30

3. 56

5. –6

7. 6,750

9. [latex]11x^2 + 17x[/latex]

11. [latex]-7y^2 + y[/latex]

13. [latex]3y^2 + 3x[/latex]

15. [latex]x^2y^2 + xy^2[/latex]

17. [latex]-90x + 42[/latex]

19. –38

21. [latex]-5x + 7[/latex]

23. [latex]2x - 4[/latex]

25. [latex]30x - 10y - 90[/latex]

27. [latex]-14y - 144[/latex]

Exercise 7.3

1. [latex]x + 6 = 10; x = 4[/latex]

3. [latex]6x = 72; x = 12[/latex]

5. [latex]\displaystyle{\frac{x}{5} = 4; x = 20}[/latex]

7. [latex]\displaystyle{\frac{2}{3}x = 12; x = 18}[/latex]

9. [latex]x = 30[/latex]

11. [latex]x = 18[/latex]

13. [latex]x = -17[/latex]

15. [latex]x = 6[/latex]

17. [latex]\displaystyle{x = 1\frac{2}{11}}[/latex]

19. [latex]\displaystyle{x = 1\frac{2}{5}}[/latex]

21. [latex]x = 2[/latex]

23. [latex]\displaystyle{x = -\frac{3}{20}}[/latex]

25. [latex]x = 4[/latex]

27. [latex]x = 24[/latex]

29. [latex]x = 16[/latex]

31. [latex]y = 1.72[/latex]

33. [latex]x = 4[/latex]

35. [latex]x = 1.8[/latex]

37. [latex]x = -2[/latex]

39. [latex]x = -2.2[/latex]

41. [latex]x = 4.33[/latex]

43. [latex]x = 0.41[/latex]

45. [latex]x = 16[/latex]

47. [latex]y = 42[/latex]

49. [latex]x = 52.6[/latex]

51. [latex]y = 11[/latex]

53. [latex]x = -5[/latex]

55. [latex]5[/latex]

57. 9-metre and 16-metre long wire

59. Becky’s share: $325; Andy’s share: $175

61. Adult ticket: $10; Child ticket: $7

63. [latex]A = (x + 4)(x + 3); A = 182[/latex] square metres

65. $12.5

67. $26

69. 30°, 70°, and 80°

71. 15 cm, 25 cm and 30 cm

73. 188.24 lb

75. Water: 2.13 L; 15% Solution: 1.87 L

Review Exercises 7

1. 1. [latex]3x + 12[/latex]
   2. [latex]x - 5[/latex]

3. 1. [latex](3 + x)x[/latex]
   2. [latex]10x + 15[/latex]

5. 1. [latex]\displaystyle{\frac{1}{x^2}}[/latex]
   2. [latex]-x^7[/latex]

7. 1. [latex]x^4[/latex]
   2. [latex]\displaystyle{\frac{1}{x^2}}[/latex]

9. 1. [latex]x^{\frac{3}{2}} y[/latex]
   2. [latex]x^2[/latex]

11. 1. [latex]5x + 17 = 42; x = 5[/latex]
    2. [latex]\displaystyle{\frac{x}{15} = 45}; x = 675[/latex]

13. 1. [latex]x - 10 = 10; x = 20[/latex]
    2. [latex]3(4x) = 36; x = 3[/latex]

15. 1. [latex]x = 3[/latex]
    2. [latex]x = 18[/latex]

17. 1. [latex]x = -9[/latex]
    2. [latex]x = 2[/latex]

Self-Test Exercises 7

1. a. [latex]3x - 25[/latex]
   b. [latex]x + 18[/latex]

2. a. [latex]2x - 6[/latex]
   b. [latex]\displaystyle{\frac{x}{3}}[/latex]

3. a. [latex]-x^2 - 6x + 10; 19[/latex]
   b. [latex]4x - 11y + 7; 4[/latex]

4. a. [latex]6x + 13; 31[/latex]
   b. [latex]-5x^2 + 26x + 24; 45[/latex]

5. a. [latex]2x - 9 = 21; x = 15[/latex]
   b. [latex]3 - 5x = 22; x = \displaystyle{-\frac{19}{5}} = -3.8[/latex]

6. a. [latex](4)(8) = 16x; x = 2[/latex]
   b. [latex]6x = 30; x = 5[/latex]

7. a. [latex]x = 4[/latex]
   b. [latex]x = 18[/latex]

8. a. [latex]\displaystyle{-\frac{4}{7}}[/latex]
   b. [latex]\displaystyle{4\frac{2}{3}}[/latex]