Student’s solutions manual : Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences. 13th Edition. . 2011. Haeussler, Ernest F.; Paul, Richard S.; Trimble, Cindy; Wood, Richard. J. (Solutions and workouts only)

, Table of Contents
Chapter 0 1
Chapter 1 35
Chapter 2 54
Chapter 3 89
Chapter 4 132
Chapter 5 160
Chapter 6 177
Chapter 7 231
Chapter 8 295
Chapter 9 333
Chapter 10 357
Chapter 11 378
Chapter 12 423
Chapter 13 469
Chapter 14 539
Chapter 15 614
Chapter 16 658
Chapter 17 670

, Chapter 0
Problems 0.1 x+2 x 2 x
7. True; = + = + 1.
2 2 2 2
1. True; –13 is a negative integer.

2. True, because −2 and 7 are integers and 7 ≠ 0. ⎛ b ⎞ ab
8. True, because a ⎜ ⎟ = .
⎝c⎠ c
3. False, because the natural numbers are 1, 2, 3,
and so on. 9. False; the left side is 5xy, but the right side is
5 x 2 y.
0
4. False, because 0 = .
1 10. True; by the associative and commutative
properties, x(4y) = (x ⋅ 4)y = (4 ⋅ x)y = 4xy.
5
5. True, because 5 = .
1 11. distributive

6. False, since a rational number cannot have 12. commutative
7
denominator of zero. In fact, is not a number 13. associative
0
at all because we cannot divide by 0. 14. definition of division

7. False, because 25 = 5, which is a positive 15. commutative and distributive
integer.
16. associative
8. True; 2 is an irrational real number.
17. definition of subtraction
9. False; we cannot divide by 0.
18. commutative
10. False, because the natural numbers are 1, 2, 3,
19. distributive
and so on, and 3 lies between 1 and 2.
20. distributive
11. True
21. 2x(y − 7) = (2x)y − (2x)7 = 2xy − (7)(2x)
12. False, since the integer 0 is neither positive nor = 2xy − (7 · 2)x = 2xy − 14x
negative.
22. (a − b) + c = [a + (−b)] + c = a + (−b + c)
Problems 0.2 = a + [c + (−b)] = a + (c − b)
1. False, because 0 does not have a reciprocal. 23. (x + y)(2) = 2(x + y) = 2x + 2y
7 3 21 24. 2[27 + (x + y)] = 2[27 + (y + x)] = 2[(27 + y) + x]
2. True, because ⋅ = = 1.
3 7 21 = 2[(y + 27) + x]

3. False; the negative of 7 is −7 because 25. x[(2y + 1) + 3] = x[2y + (1 + 3)] = x[2y + 4]
7 + (−7) = 0. = x(2y) + x(4) = (x · 2)y + 4x = (2x)y + 4x
= 2xy + 4x
4. False; 2(3 · 4) = 2(12) = 24, but
(2 · 3)(2 · 4) = 6 · 8 = 48. 26. (1 + a)(b + c) = 1(b + c) + a(b + c)
= 1(b) + 1(c) + a(b) + a(c) = b + c + ab + ac
5. False; –x + y = y + (–x) = y – x.

6. True; (x + 2)(4) = (x)(4) + (2)(4) = 4x + 8.

1

, Chapter 0: Review of Algebra ISM: Introductory Mathematical Analysis


27. x(y − z + w) = x[(y − z) + w] = x(y − z) + x(w) 51. X(1) = X
= x[y + (−z)] + xw = x(y) + x(−z) + xw
= xy − xz + xw 52. 3(x – 4) = 3(x) – 3(4) = 3x – 12

28. –2 + (–4) = –6 53. 4(5 + x) = 4(5) + 4(x) = 20 + 4x

29. –6 + 2 = –4 54. –(x – 2) = –x + 2

30. 6 + (–4) = 2 55. 0(–x) = 0

31. 7 – 2 = 5 ⎛ 1 ⎞ 8 ⋅1 8
56. 8 ⎜ ⎟ = =
⎝ 11 ⎠ 11 11
32. 7 – (–4) = 7 + 4 = 11
5
33. −5 − (−13) = −5 + 13 = 8 57. =5
1
34. −a − (−b) = −a + b
14 x 2 ⋅ 7 ⋅ x 2 x
58. = =
35. (–2)(9) = –(2 · 9) = –18 21 y 3 ⋅ 7 ⋅ y 3 y

36. 7(–9) = –(7 · 9) = –63 3 3 3
59. = =−
37. (–2)(–12) = 2(12) = 24 −2 x −(2 x) 2x

38. 19(−1) = (−1)19 = −(1 · 19) = −19 2 1 2 ⋅1 2
60. ⋅ = =
3 x 3 ⋅ x 3x
−1 ⎛ 9⎞
39. = −1⎜ − ⎟ = 9
−9
1 ⎝ 1⎠ a a(3b) 3ab
61. (3b) = =
c c c
40. –(–6 + x) = –(–6) – x = 6 – x
⎛ 7 ⎞
41. –7(x) = –(7x) = –7x 62. (5a ) ⎜ ⎟ = 7
⎝ 5a ⎠
42. –12(x – y) = (–12)x – (–12)(y) = –12x + 12y
(or 12y – 12x) −aby −a ⋅ by by
63. = =
−ax −a ⋅ x x
43. –[–6 + (–y)] = –(–6) – (–y) = 6 + y
7 1 7 ⋅1 7
−3 3 1⋅ 3 1 64. ⋅ = =
44. −3 ÷ 15 = =− =− =− y x y ⋅ x xy
15 15 5⋅3 5
2 5 2 ⋅ 5 10
−9 9 9 ⋅1 1 65. ⋅ = =
45. −9 ÷ (−27) = = = = x y x ⋅ y xy
−27 27 9 ⋅ 3 3
1 1 3 2 3+ 2 5
−a a 66. + = + = =
46. (−a ) ÷ (−b) = = 2 3 6 6 6 6
−b b

47. 2(–6 + 2) = 2(–4) = –8 5 3 5 9 5 + 9 14 2 ⋅ 7 7
67. + = + = = = =
12 4 12 12 12 12 2 ⋅ 6 6
48. 3[–2(3) + 6(2)] = 3[–6 + 12] = 3[6] = 18
3 7 9 14 9 − 14 −5 5 ⋅1 1
49. (–2)(–4)(–1) = 8(–1) = –8 68. − = − = = =− =−
10 15 30 30 30 30 5⋅6 6
50. (−12)(−12) = (12)(12) = 144


2