Solution manual for intermediate algebra 1st edition by bracken

Since any real number multiplied by itself always results in either 0 or a positive number, there is no number that can be multiplied by itself to give −100.. Since x can be any number l

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15. No Whole numbers larger than 5 are elements in set

F, but are not elements of set G

16. Yes Every element in set G is a whole number

17. No The elements blue and red are part of set E, but

are not part of set D

18. Yes Both elements in set D are also part of set E

19. Yes Every integer can be written as a ratio of two

integers (For example, 17 can be written as 17

1 )

20. Yes Every irrational number is a real number

21. Yes No irrational number is also a rational number

22. No The set of integers has every one of its elements in

common with the set of rational numbers

0.399

23410.2341

Integers

Whole numbers NOT FOR SALE AMENTALS OF AMENTALS O R25 25

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Chapter 1 Fundamentals of Algebra

84. Since any real number multiplied by itself always results in either 0 or a positive number, there is no number that can be multiplied by itself to give −100

So 100 cannot be a real number

85. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

86. 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25

10 2414

y

89.

3 3 3

12 24

5 112628

35 20

4 755115125

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y

3 10 8 16

30 8 1622

y

2 2

103.a They took the square root of 16 and made it negative.

103.b Not a real number

104.a They listed 1 as a prime number

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© ¹

2 0.3 30.7 1

9 18 0.5 58.5 13

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1.2 Algebraic Expressions

3.5 2 3 203.5 2 3.5 3 3.5 20

43. Yes, since the sum of a real number and its additive

inverse always equals 0, and 0 is the additive identity

of the real numbers

44. Yes, since the product of a real number and its

multiplicative inverse always equals 1, and 1 is the multiplicative identity of the real numbers

5 5

7 7

47. If we consider 12 6y , it is equal to 2 since 2 6 12

Similarly 3 0y is equal to some number only if that number multiplied by 0 is equal to 3 But we know that multiplying zero by any number gives an answer

of zero This means there is no number that can equal

9 5 3

4 3

u x u

6 2 3

4 3

c d c

3 4 12

x

x x

56.

3 5

5 3 15

a

a a

57.

6 4 6

63.

3

3 3 3

228

4464

4 9 5 5

1

h h h h

6 10 4 4

1

p p p p

x

68. 5 0

5 15

2 2 0

1

z z z z

70.

6 6

6 6 0

1

p p p p

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4 1 15 8

3 7

x y xy

x y

3 7 9 3

4 6 6 4 6 4

1243133

a b

a b b a b a

2 72

9 6 2 13

3 11

3 11 3 11

15715

x y

x y x y

3 41211212

x y x y

x y y x y x

15

2 71411414

k k

p

p p k k

111

0 8

4 4

0 32 32 32

111

0 12

0 60 60 60

111

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1.3 Equations and Inequalities in One Variable

9 4

25 736175

4 2

25 78

z z

8 3 5

z z z z

7 3 21

x

x x

98.a They subtracted the exponent of the numerator from

the exponent of the denominator

98.b

7 10

7 10 3 3

1

x x x x

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x x

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Algebra

18 a 8 w 1212 3434 18 b

O

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c

c c

d

d d

15

60320

60154

15 15

32.a.

4605

60

300475

300604

60 60

33.a. 0.8 1.9 1.9 1.91.1

34.a. 0.29 0.81

0.81 0.810.52

35.a.

150.3

0.34.5

15 15

36.a.

120.7

0.78.4

12 12

NOT FOR SALE1.3 Equations and 1.3 Equations an

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343

434

k k

z z

a

2

353

66

48

480860

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c c c c

p p p p

Solution: The set of real numbers

51.b Check with c and 0 c : 1

51 b

51 Check with c 0 and c

R

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55.b Check with n 0 and n 1:

56.b Check with u 0 and u 1:

33

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2

27 183

3 183

181

12108

9 9

62.a.

615

1590

1515

1616

160155

3323

15

2272

20

NOT FOR SALE R 1.3 Equations and 1.3 Equations an

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68.b Check with x 0 and x 1:

a

a a

c

c c

216

v

v v

424

q

q q

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z z

z z z z

p p p p

17 17

17 10 242

80. Both sides of the equation are identical, so any x value

placed in the left hand side of the equation will produce the same result when placed in the right hand side of the equation

81 Answers will vary One possible answer is:

83 Solving an equation in one variable:

1 Apply the distributive property to clear all parentheses (and other grouping symbols) on both sides of the equation

2 Combine like terms on each side of the equation

3 Use the addition and/or subtraction properties of equality to get all variable terms on one side of the equals sign and all constant terms on the other side

4 Use the multiplication and/or division properties of equality to make the coefficient of the variable equal to 1

84 Clearing fraction from an equation in one variable:

1 Find the least common multiple of all denominators

of all fractions in the problem

2 Multiply both sides of the equation by the least common multiple

3R

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85. Since x can be any number larger than 6, the interval

begins at 6 and goes to positive infinity Since 6 is not

part of the solution, use a ( on the left side of the

interval When infinity is a right endpoint of an

interval, that side of the interval always uses a ) So

the interval is written (6, ∞)

86. Since x can be any number smaller than 2 or equal to 2,

the interval begins at negative infinity and continues to

2 Since 2 is part of the solution, use a ] on the right

side of the interval When negative infinity is a left

endpoint of an interval, that side of the interval always

uses a ( So the interval is written (−∞, 2]

87. Since x can be any number smaller than 2 or equal to 2,

the number line is shaded beginning at negative infinity

and continuing to 2 Since 2 is part of the solution, use

a ] on the right side of the shaded line

88. Since x can be any number larger than 6, the number

line is shaded beginning at 6 and continuing to positive

infinity Since 6 is not part of the solution, use a ( on

the left side of the shaded line

x

d

ddd

89.b Check with any number less than or equal to 8

x

d

ddd

90.b Check with any number less than or equal to 7.

ber larger than 6 the interval

ber larger than 6 the interva O91 a 1 3 99 1515

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t

95.b Check with any number greater than or equal to −2.

Letting x 0:

t

96.b Check with any number greater than or equal to −1.

Letting x 0:

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101.b Check with any number greater than −84.

x x

272

3156

x

x x

2 95

x

x x

d

107.b Check with any number less than or equal to 10

9

Letting x 2:

2 50

9 9409

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107.c 10

,9

3 85

z

z z

d

108.b Check with any number less than or equal to 15

8

Letting z 2:

2 50

0

c c

c

d

t

112.b Check with any number less than or equal to 0

Letting c : 1

0 8

d d

x x

x

tt

t

113.b Check with any number greater than or equal to 3

2 Letting x 2:

x x

111 b Check with any number lCheck with any number l

R

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115.b Check with any number greater than 0

tt

120.c [441, ∞) 121.a. 15

16 33615

121.c (315, ∞) 122.a. 11

12 27611

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122.b Check with any number greater than 253

mber greater than 253

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m

m m

4 61.666 1

n

n n

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134.b Check with any number greater than 9

6 41.08333 1

k k

2752

h h

w

w w

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137.c 41

,6

m

m m

h h

c c

Chapter Fundamentals of Algebra

x x

NOT FOR SALE

Algebra< /b>

18 a... p p

51.b Check with c and c :

NOT FOR SALE1.3...

Similarly 0y is equal to some number only if that number multiplied by is equal to But we know that multiplying zero by any number gives an answer

of zero This means there is no number

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