Ecuaciones

Chapter

R

Review
R.1
1. 3. 5. 6. 7. 8. 9.

Real Numbers
Rational Distributive True False, the Zero Product Property states that if a ⋅ b = 0, then a = 0, or b = 0, or both. False, the least common multiple of 12 and 18 is 36. True (a) (b) (c) (d) (e) 2. 4. 4 + 5 ⋅ 6 − 3 = 4 + 30 − 3 = 34 − 3 = 31 5( x + 3) = 6

{2,5} {−6,2,5}

10.

(a) (b) (c) (d) (e)

 1  −6, ,−1.333...,2,5  2  {π}  1  −6, −1.333...,π,2,5   2 

{ }

 5  − ,2.060606...,1.25,0,1  3  5  5  − ,2.060606...,1.25,0,1, 5   3 

{1} {0,1}

11.

(a) (b) (c) (d) (e)

 1 1 1 0,1, , ,   2 3 4 None  1 1 1 0,1, , ,   2 3 4

{1} {0,1}

12.

(a) (b) (c) (d) (e)

{−1} {−1,−1.1,−1.2,−1.3}
None {−1,−1.1,−1.2,−1.3}

None

1

Chapter R
13. (a) (b) (c) (d) (e)Review
14. (a) (b) None None 1  (c)  +10.3 2  (d) − 2, π + 2   1 (e)  − 2, π + 2, +10.3   2

None None None  1  2, π, 2 +1,π +   2  1  2, π, 2 +1,π +   2 16. (a) 25.861 (b) 25.861 19. (a) 0.063 (b) 0.062 22. (a) 1.001 (b) 1.000 25. (a) 34.733 (b) 34.733 28. 31. 34. 5 ⋅2 =10 3y =1+ 2 2− y = 6

{

}

15. (a) 18.953 (b) 18.952 18. (a) 99.052 (b) 99.052 21. (a)9.999 (b) 9.998 24. (a) 0.556 (b) 0.555 27. 3+2=5

17. (a) 28.653 (b) 28.653 20. (a) 0.054 (b) 0.053 23. (a) 0.429 (b) 0.428 26. (a) 16.200 (b) 16.200 29. 32. 35. x + 2 = 3⋅ 4 2x = 4 ⋅ 6 x =6 2 6−4 + 3=2+ 3=5 4 + 5 − 8 = 9 − 8 =1 2− 1 4−1 3 = = 2 2 2

30. 3+ y = 2 + 2 33. x −2= 6 2 =6 x −6 + 4 ⋅ 3 = −6 +12 = 6 8 − 3 − 4 = 5 − 4 =1 6 − [3⋅5 + 2⋅ ( 3 − 2)] = 6 − [15 + 2 ⋅ (1)] = 6 −17 = −11

36.39. 42. 45.

37. 40. 43. 46.

9−4 + 2=5+ 2 =7 8 − 4 ⋅ 2 = 8 −8 = 0 4+ 1 12 + 1 13 = = 3 3 3

38. 41. 44. 47.

2 ⋅ [8 − 3( 4 + 2)] − 3 = 2 ⋅ [8 − 3⋅ (6)] − 3 = 2 ⋅ [8 −18] − 3 = 2 ⋅ [−10] − 3 = −20 − 3 = −23

2( 3 − 5) + 8 ⋅ 2 −1 = 2 ⋅ (−2) + 16 −1 = −4 + 16 −1 = 12 −1 = 11

2

Section R.1
48. 1− ( 4 ⋅ 3 − 2 + 2) = 1− (12 − 2 + 2) = 1− (10 + 2) = 1−12 = −11 49. 10 − [6 − 2 ⋅2 + (8 −3)] ⋅2 = 10 − [6 − 4 + 5] ⋅ 2 = 10 − [2 + 5] ⋅ 2 = 10 − [ 7] ⋅ 2 = 10 −14 = −4 1 2 52. 50.

Real Numbers

= 2 − 20 − [6 ⋅ (−1)] = −18 − [−6] = −18 + 6 = −12 4 + 8 12 = =6 5− 3 2

2 − 5 ⋅ 4 − [6( 3 − 4 )]

51.

(5 − 3) = (2) =1
2 − 4 −2 = = −1 5− 3 2

1 2

(5 + 4 ) = (9) = 3
3 10 3⋅ 2 ⋅ 5 2 ⋅ = = 5 21 5 ⋅ 3⋅ 7 7

1 3

1 3

53.

54.

55.

56.

5 3 5⋅ 3 ⋅ = 9 10 3⋅ 3⋅ 2⋅ 5 1 1 = = 3⋅ 2 6 3 2 15 + 8 23 + = = 4 5 20 20

57.

6 10 3⋅ 2 ⋅ 5 ⋅ 2 ⋅ = 25 27 5 ⋅ 5 ⋅ 9 ⋅ 3 2⋅ 2 4 = = 5 ⋅ 9 45 4 1 8 + 3 11 + = = 3 2 6 6 5 1 10 + 3 13 + = = 18 12 36 36

58.

21 100 3⋅ 7 ⋅ 5 ⋅ 5 ⋅ 2 ⋅ 2 ⋅ = 25 3 5⋅ 5⋅ 3 = 7 ⋅ 2 ⋅ 2 = 28 5 9 25 + 54 79 + = = 6 5 30 30 2 8 6 + 40 46 + = = 15 9 45 45

59.

60.

61.

62.

8 15 16 + 135 151 + = = 9 2 18 18 1 7 3 − 35 − = 30 18 9032 16 =− =− 90 45 6 3 12 − 15 3 − = =− 35 14 70 70 6( x + 4 ) = 6x + 24

63.

64.

65.

66.

3 2 9− 4 5 − = = 14 21 42 42 5 18 = 5 ⋅ 27 11 18 11 27 5 3⋅ 9 = ⋅ 2 ⋅ 9 11 15 = 22

67.

3 2 9− 8 1 − = = 20 15 60 60 5 21 = 5 ⋅ 35 2 21 2 35 5 5⋅ 7 = ⋅ 3⋅ 7 2 25 = 6

68. 71.

69.

70.

72. 4(2x −1) = 8x − 4 73. 74. x ( x − 4) = x 2 − 4x 4x ( x + 3) = 4x 2 + 12x

75.

( x + 2)(x + 4 )
= x + 4x + 2x + 8
2

76.

( x + 5)( x +1)
= x + x + 5x + 5
2

77.

( x −2)( x +1)
= x 2 + x − 2x − 2 = x 2 − x −2

= x 2 + 6x + 8

= x 2 + 6x + 5

3

Chapter R
78.

Review
79.

( x − 4)( x +1)
= x + x − 4x − 4
2

( x −8)( x − 2)
= x − 2x − 8x +16
2

80.

( x − 4)( x − 2)
= x 2 − 2x − 4 x + 8 = x 2 − 6x + 8 5x = (2 + 3) x = 2x + 3x

= x 2 − 3x − 481.

= x 2 −10x +16 82.

( x + 2)( x −2)
= x − 2x + 2x − 4
2

( x − 3)( x + 3)
= x + 3x − 3x − 9
2

83.

= x2 − 4 84.

= x2 − 9

2 + 3⋅ 4 = 2 +12 = 14 since multiplication comes before addition in the Order of Operations for real numbers. (2 + 3) ⋅ 4 = 5⋅ 4 = 20 since operations inside parentheses come before multiplication in the Order of Operations for real numbers. 2(3⋅ 4) =...