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 7.3

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]

29. [latex] -7y^2 - 12y + 6 [/latex]

31. [latex] 4x + 25 [/latex]

33. [latex] -17x^2 + 58x - 36 [/latex]

35. [latex] 10x^2 - 16x - 14 [/latex]

37. [latex] -8x^2 - 16x + 15 [/latex]

39. [latex] x^2 + 10x + 25 [/latex]

41. [latex] 4x^2 + 9y^2 + 12xy [/latex]

43. [latex] x^2 - 6x + 9 [/latex]

45. [latex] 9x^2 + 4y^2 - 12xy [/latex]

47. [latex] 9x^2 - 6x + 1 [/latex]

49. [latex] 4x^2 - 12x + 9 [/latex]

51. [latex] x^2 - 25 [/latex]

53. [latex] -49x^2 + 9 [/latex]

55. [latex] 2x^2 + 2x + 13 [/latex]

57. [latex] 8x + 25 [/latex]

59. [latex] 13x^2 - 12x - 5 [/latex]

61. [latex] 4x^2 - y^2 - 16x - 6y + 7 [/latex]

63. [latex] 4 [/latex]

65. [latex] \displaystyle{\frac{3}{2}} [/latex]

67. [latex] -x - y [/latex]

69. [latex] 5x - 3y + 1 [/latex]

71. [latex] \displaystyle{\frac{x^2}{2y}} [/latex]

Exercise 7.5

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] x^2 [/latex]

       
       

    2. [latex] 1 [/latex]

       
       

13. 1. [latex] 3x^7 [/latex]

       
       

    2. [latex] x^4 [/latex]

       
       

15. 1. [latex] \displaystyle{\frac{x^4}{4y^5}} [/latex]

       
       

    2. [latex] \displaystyle{\frac{2y^{10}}{x^7}} [/latex]

       
       

17. 1. [latex] \displaystyle{\frac{8x^9}{y^6}} [/latex]

       
       

    2. [latex] 2x^2 [/latex]

       
       

19. 1. [latex] x^{14} [/latex]

       
       

    2. [latex] \displaystyle{\frac{y^{24}}{4x^{10}}} [/latex]

       
       

21. 1. 12

       
       

    2. -12

       
       

23. 1. -32

       
       

    2. 10

       
       

25. 1. -24

       
       

    2. 91

       
       

27. 1. [latex] 2x(3x - 2); 2 [/latex]

       
       

    2. [latex] 7x(y + 2x); 168 [/latex]

       
       

29. 1. [latex] (3x - 1)(2x^2 + 5) [/latex]

       
       

    2. [latex] (x - 3)(y + 5) [/latex]

       
       

31. 1. [latex] (2x - 3)(2x + 3) [/latex]

       
       

    2. [latex] (5x - 8y)(5x + 8y) [/latex]

       
       

33. 1. [latex] (x + 9)(x - 4) [/latex]

       
       

    2. [latex] (2x + 5)(2x + 3) [/latex]

       
       

35. 1. [latex] (x + 8)(x + 8) [/latex]

       
       

    2. [latex] (3x - 4)(3x - 4) [/latex]

       
       

37. 1. [latex] 5x + 17 = 42; x = 5 [/latex]

       
       

    2. [latex] \displaystyle{\frac{x}{15} = 45}; x = 675 [/latex]

       
       

39. 1. [latex] x - 10 = 10; x = 20 [/latex]

       
       

    2. [latex] 3(4x) = 36; x = 3 [/latex]

       
       

41. 1. [latex] x = 3 [/latex]

       
       

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

       
       

43. 1. [latex] x = -9 [/latex]

       
       

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

       
       

Self-Test Exercises 7

1. 1. [latex] 3x - 25 [/latex]

      
      

   2. [latex] x + 18 [/latex]

      
      

2. 1. [latex] 2x - 6 [/latex]

      
      

   2. [latex] \displaystyle{\frac{x}{3}} [/latex]

      
      

3. 1. [latex] -x^7 [/latex]

      
      

   2. [latex] x^2 [/latex]

      
      

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

      
      

   2. [latex] x^2 [/latex]

      
      

5. 1. [latex] 4y^2 [/latex]

      
      

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

      
      

6. 1. [latex] -x^2 - 6x + 10; 19 [/latex]

      
      

   2. [latex] 4x - 11y + 7; 4 [/latex]

      
      

7. 1. [latex] 6x + 13; 31 [/latex]

      
      

   2. [latex] -5x^2 + 26x + 24; 45 [/latex]

      
      

8. 1. [latex] 2xy(4y - 3x) [/latex]

      
      

   2. [latex] 2b(5a - 4c) [/latex]

      
      

9. 1. [latex] (x - 5)(4y - x) [/latex]

      
      

   2. [latex] (1 - 11x)(1 + 11x) [/latex]

      
      

10. 1. [latex] 2(x - 4)(x - 7) [/latex]

       
       

    2. [latex] (4x + 3)(x - 3) [/latex]

       
       

11. 1. [latex] (x + 5)(x + 5) [/latex]

       
       

    2. [latex] (x + 8y)(x - 2y) [/latex]

       
       

12. 1. [latex] 2x - 9 = 21; x = 15 [/latex]

       
       

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

       
       

13. 1. [latex] (4)(8) = 16x; x = 2 [/latex]

       
       

    2. [latex] 6x = 30; x = 5 [/latex]

       
       

14. 1. [latex] x = 4 [/latex]

       
       

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

       
       

15. 1. [latex] \displaystyle{-\frac{4}{7}} [/latex]

       
       

    2. [latex] \displaystyle{4\frac{2}{3}} [/latex]