Contents

Preface
1Foundations
- Introduction
- 1.1Use the Language of Algebra
- 1.2Integers
- 1.3Fractions
- 1.4Decimals
- 1.5Properties of Real Numbers
- Chapter Review
  Key Terms
  Key Concepts
- Exercises
  Review Exercises
  Practice Test
2Solving Linear Equations
3Graphs and Functions
4Systems of Linear Equations
5Polynomials and Polynomial Functions
6Factoring
7Rational Expressions and Functions
8Roots and Radicals
9Quadratic Equations and Functions
10Exponential and Logarithmic Functions
11Conics
12Sequences, Series and Binomial Theorem
- Introduction
- 12.1Sequences
- 12.2Arithmetic Sequences
- 12.3Geometric Sequences and Series
- 12.4Binomial Theorem
- Chapter Review
  Key Terms
Answer Key
Index

Chapter 2

Try It

Show solution

2.1

ⓐ no ⓑ yes

Show solution

2.2

ⓐ yes ⓑ no

Show solution

2.3

$m = 2 m = 2$

Show solution

2.4

$a = 0 a = 0$

Show solution

2.5

$u = 2 u = 2$

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2.6

$x = 4 x = 4$

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2.7

$p = −2 p = −2$

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2.8

$q = −8 q = −8$

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2.9

$y = - \frac{17}{5} y = - \frac{17}{5}$

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2.10

$z = 0 z = 0$

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2.11

identity; all real numbers

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2.12

identity; all real numbers

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2.13

conditional equation; $q = - \frac{9}{11} q = - \frac{9}{11}$

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2.14

conditional equation; $k = \frac{201}{14} k = \frac{201}{14}$

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2.15

contradiction; no solution

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2.16

contradiction; no solution

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2.17

$x = \frac{1}{2} x = \frac{1}{2}$

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2.18

$x = −2 x = −2$

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2.19

$x = 12 x = 12$

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2.20

$u = −12 u = −12$

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2.21

$n = 2 n = 2$

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2.22

$m = −1 m = −1$

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2.23

$r = 1 r = 1$

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2.24

$s = −8 s = −8$

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2.25

$n = 9 n = 9$

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2.26

$d = 16 d = 16$

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2.27

He bought two notebooks.

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2.28

He did seven crosswords puzzles.

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2.29

$33$

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2.30

$66$

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2.31

$−15, −8 −15, −8$

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2.32

$−29, 11 −29, 11$

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2.33

$−33, −32, −31 −33, −32, −31$

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2.34

$−13, −12, −11 −13, −12, −11$

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2.35

32, 34, 36

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2.36

$−10, −8, −6 −10, −8, −6$

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2.37

The average cost was $5,000.

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2.38

The median price was $19,300.

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2.39

ⓐ 36 ⓑ $26 ⓒ $125 % 125 %$

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2.40

ⓐ 33 ⓑ $36 ⓐ $175 % 175 %$

Show solution

2.41

25 grams

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2.42

2,375 mg

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2.43

50%

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2.44

40%

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2.45

$8.8 % 8.8 %$

Show solution

2.46

50%

Show solution

2.47

ⓐ $600 ⓑ $1,800

Show solution

2.48

ⓐ $2,975 ⓑ $11,475

Show solution

2.49

He will earn $2,500.

Show solution

2.50

She earned $7,020.

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2.51

The rate of simple interest was 6%.

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2.52

The rate of simple interest was 5.5%.

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2.53

He paid $17,590.

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2.54

She deposited $9,600.

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2.55

$b = \frac{2 A}{h} b = \frac{2 A}{h}$

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2.56

$h = \frac{2 A}{b} h = \frac{2 A}{b}$

Show solution

2.57

$C = \frac{5}{9} (F - 32) C = \frac{5}{9} (F - 32)$

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2.58

$b = \frac{2 A - B h}{h} b = \frac{2 A - B h}{h}$

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2.59

$t = \frac{A - P}{P r} t = \frac{A - P}{P r}$

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2.60

$r = \frac{A - P}{P t} r = \frac{A - P}{P t}$

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2.61

$y = \frac{9 - 4 x}{7} y = \frac{9 - 4 x}{7}$

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2.62

$y = \frac{1 - 5 x}{8} y = \frac{1 - 5 x}{8}$

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2.63

The window’s height is 12 meters.

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2.64

The length of the base is 6 feet.

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2.65

The measures of the angles are 20°, 70°, and 90°.

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2.66

The measures of the angles are 30°, 60°, and 90°.

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2.67

The length of the leg is 8.

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2.68

The length of the leg is 12.

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2.69

The length is 16 inches and the width is 39 inches.

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2.70

The length is 17 yards and the width is 26 yards.

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2.71

The lengths of the sides of the triangle are 5, 11 and 12 inches.

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2.72

The lengths of the sides of the triangle are 4, 7 and 9 feet.

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2.73

The length of the swimming pool is 70 feet and the width is 30 feet.

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2.74

The length of the garden is 90 yards and the width is 60 yards.

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2.75

The ladder reaches 12 feet.

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2.76

He should attach the lights 8 feet from the base of the mast.

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2.77

Jess has 41 nickels and 18 quarters.

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2.78

Elane has 22 nickels and 59 dimes.

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2.79

Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.

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2.80

Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.

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2.81

84 adult tickets, 31 student tickets

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2.82

615 children’s tickets and 195 adult tickets

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2.83

Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

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2.84

Becca mixed 21 gallons of fruit punch and seven gallons of soda.

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2.85

The speed of the local train is 48 mph and the speed of the express train is 60 mph.

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2.86

Jeromy drove at a speed of 80 mph and his mother drove 60 mph.

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2.87

Christopher’s speed was 50 mph and his parents’ speed was 40 mph.

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2.88

Ashley’s parents drove 55 mph and Ashley drove 62 mph.

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2.89

Pierre and Monique will be 429 miles apart in 3 hours.

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2.90

Thanh and Nhat will be 330 miles apart in 2.2 hours.

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2.91

Suzy’s speed uphill is $1.8 1.8$ mph and downhill is three mph.

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2.92

The boat’s speed upstream is eight mph and downstream is12 mph.

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2.93

Hamilton drove 40 mph in the city and 70 mph in the desert.

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2.94

Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.

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2.95

ⓐ

ⓑ

The graph of the inequality x is less than or equal to negative 1.5 is indicated on a number line with a right bracket at negative 1.5 and shading to the left. The solution in interval notation is the interval from negative infinity to negative 1.5 enclosed within a left parenthesis and right bracket.

ⓒ

The graph of the inequality x is greater than or rqual to three-fourths is indicated on a number line with a left bracket at three-fourths and shading to the right. The solution in interval notation is the interval from three-fourths to infinity enclosed within a left bracket and left parentheses.

Show solution

2.96

ⓐ

ⓑ

ⓒ

The graph of the inequality x is less than negative two-thirds is indicated on a number line with a right parenthesis at negative two-thirds and shading to the left. The solution in interval notation is the interval from negative infinity to negative two-thirds enclosed within parentheses.

Show solution

2.97

ⓐ

Negative 2 is less x which is less than 1. There are open circles at negative 2 and 1 and shading between negative 2 and 1 on the number line. Put parentheses at negative 2 and 1. Write in interval notation.

ⓑ

Negative 5 is less than or equal to x which is less than negative 4. There is a closed circle at negative 6 and an open circle at negative 4 and shading between negative 5 and negative 4 on the number line. Put a bracket at negative 5 and a parenthesis at negative 4. Write in interval notation.

ⓒ

1 is less than or equal to x which is less than 4.25. There is closed circle at 1 and a closed circle at 4.25 and shading between 1 and 4.25 on the number line. Put brackets at 1 and 4.25. Write in interval notation.

Show solution

2.98

ⓐ

Negative 6 is less than x which is less than 2. There is an open circle at negative 6 and an open circle at 2 and shading between negative 6 and 2 on the number line. Put parentheses at negative 6 and 2. Write in interval notation.

ⓑ

Negative 3 is less than or equal to x which is less than negative 1. There is a closed circle at negative 3 and an open circle at negative 1 and shading between negative 3 and negative 1 on the number line. Put a bracket at negative 3 and a parenthesis at negative 1. Write in interval notation.

ⓒ

2.5 is less than or equal to x which is less thanor equal to 6. There is a closed circle at 2.5 and a closed circle at 6 and shading between 2.5 and 6 on the number line. Put brackets at 2.5 and 6. Write in interval notation.

Show solution

2.99

ⓐ

p is less than eleven-twelfths. The solution on the number line has a right bracket at eleven-twelfths with shading to the right. The solution in interval notation is, eleven-twelfths to infinity within a bracket and parenthesis.

ⓑ

c is less than 8. The solution on the number line has a left bracket at 8 with shading to the right. The solution in interval notation is, 8 to infinity within parentheses.

ⓒ

m is greater than or equal to 8. The solution on the number line has a right bracket at 64 with shading to the right. The solution in interval notation is, 64 to infinity within a bracket and parentheses.

Show solution

2.100

ⓐ

r is less than or equal to eleven-twelfths. The solution on the number line has a left bracket at eleven-twelfths with shading to the left. The solution in interval notation is negative infinity to eleven-twelfths within a parenthesis and a bracket.

ⓑ

c is less than or equal to 5. The solution on the number line has a right bracket at 5 with shading to the left. The solution in interval notation is negative infinity to 5 within a parentheses and a bracket.

ⓒ

n is greater than negative 18. The solution on the number line has a left parenthesis at negative 18 with shading to the right. The solution in interval notation is negative 18 to infinity within parentheses.

Show solution

2.101

ⓐ

q is greater than or equal to negative 4. The solution on the number line has a left parenthesis at negative 4 with shading to the right. The solution in interval notation is negative 4 to infinity within parentheses.

ⓑ

k is greater than or equal to negative 180. The solution on the number line has a left bracket at negative 180 with shading to the right. The solution in interval notation is negative 180 to infinity within a bracket and a parenthesis.

Show solution

2.102

ⓐ

r is greater than or equal to 10. The solution on the number line has a left bracket at 10 with shading to the right. The solution in interval notation is 10 to infinity within a bracket and parenthesis.

ⓑ

u is less than or equal to 64. The solution on the number line has a right bracket at 64 with shading to the left. The solution in interval notation is negative infinity to 64 within parenthesis and a bracket.

Show solution

2.103

q is less than or equal to 23 divided by 4. The solution on the number line has a right bracket at 23 divided by 4 with shading to the left. The solution in interval notation is negative infinity to 23 divided by 4 within a parenthesis and a bracket.

Show solution

2.104

x is greater than negative 19 divided by 4. The solution on the number line has a left parenthesis at negative 19 divided by 4 with shading to the right. The solution in interval notation is negative 19 divided by 4 to infinity within parentheses.

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2.105

y is greater than negative 6. The solution on the number line has a left parenthesis at negative 6 with shading to the right. The solution in interval notation is negative 6 to infinity within parentheses.

Show solution

2.106

u is greater than negative 10. The solution on the number line has a left parenthesis at 10 with shading to the right. The solution in interval notation is 10 to infinity within parentheses.

Show solution

2.107

The inequality is an identity. Its solution on the number line is shaded for all values. The solution in interval notation is negative infinity to infinity within parentheses.

Show solution

2.108

Show solution

2.109

The inequality is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation.

Show solution

2.110

Show solution

2.111

p minus 19 is greater than or equal to 47. Its solution is p is greater than or equal to 66. The solution on the number line has a left bracket at 66 with shading to the right. The solution in interval notation is 66 to infinity within a bracket and a parenthesis.

Show solution

2.112

a plus 4 is less than or equal to 15. Its solution is a is less than or equal to 11. The solution on the number line has a right bracket at 11with shading to the left. The solution in interval notation is negative infinity to 11 within a parenthesis and bracket.

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2.113

Angie can buy 7 packs of juice.

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2.114

Daniel can have 11 people at the party.

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2.115

Sergio and Lizeth can travel no more than 500 miles.

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2.116

Rameen can use no more than 76 therms.

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2.117

Caleb must work at least 96 hours.

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2.118

Elliot must work at least 85 jobs.

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2.119

Brenda must babysit at least 27 hours.

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2.120

Josue must shovel at least 20 driveways.

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2.121

The solution is negative 1 is less than or equal to x which is less than 4. On a number line it is shown with a closed circle at negative 1 and an open circle at 4 with shading in between the closed and open circles. Its interval notation is negative 1 to 4 within a bracket and a parenthesis.

Show solution

2.122

The solution is negative 2 is less than or equal to x which is less than 3. On a number line it is shown with a closed circle at negative 2 and an open circle at 3 with shading in between the closed and open circles. Its interval notation is negative 2 to 3 within a bracket and a parenthesis.

Show solution

2.123

The solution is x is less than three-halves. On a number line it is shown with an open circle at three-halves with shading to its left. Its interval notation is negative infinity to three-halves within a parentheses.

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2.124

The solution is x is less than negative 1. On a number line it is shown with an open circle at 1 with shading to its left. Its interval notation is negative infinity to negative 1 within parentheses.

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2.125

The inequality is a contradiction. So, there is no solution. As a result, there is no graph of the number line or interval notation.

Show solution

2.126

The inequality is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.

Show solution

2.127

The solution is negative 1 is less than or equal to x which is less than 2. Its graph has a closed circle at negative 1 and an open circle at 2 with shading between the closed and open circles. Its interval notation is negative 1 to 2 within a bracket and a parenthesis.

Show solution

2.128

The solution is 1 is less than x which is less than or equal to 3. Its graph has an open circle at 1 and a closed circle at 3 with shading between the closed and open circles. Its interval notation is negative 1 to 3 within a parenthesis and a bracket.

Show solution

2.129

The solution is x is greater than or equal to 2 or x is less than or equal to 1. The graph of the solutions on a number line has a closed circle at negative 1 and shading to the left and a closed circle at 2 with shading to the right. The interval notation is the union of negative infinity to negative 1 within a parenthesis and a bracket and 2 and infinity within a bracket and a parenthesis.

Show solution

2.130

The solution is x is greater than or equal to 1 or x is less than or equal to negative 1. The graph of the solutions on a number line has a closed circle at negative 1 and shading to the left and a closed circle at 1 with shading to the right. The interval notation is the union of negative infinity to negative 1 within a parenthesis and a bracket and 1 and infinity within a bracket and a parenthesis.

Show solution

2.131

The solution is an identity. Its solution on the number line is shaded for all values. The solution in interval notation is negative infinity to infinity within parentheses.

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2.132

Show solution

2.133

The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.

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2.134

The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.

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2.135

ⓐ $± 2 ± 2$ ⓑ no solution ⓒ 0

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2.136

ⓐ $± 11 ± 11$ ⓑ no solution ⓒ 0

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2.137

$x = 4, x = - \frac{2}{3} x = 4, x = - \frac{2}{3}$

Show solution

2.138

$x = −1, x = \frac{5}{2} x = −1, x = \frac{5}{2}$

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2.139

$x = 8, x = 0 x = 8, x = 0$

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2.140

$x = 8, x = 2 x = 8, x = 2$

Show solution

2.141

No solution

Show solution

2.142

No solution

Show solution

2.143

$x = - \frac{2}{5}, x = - \frac{2}{5},$ $x = \frac{5}{2} x = \frac{5}{2}$

Show solution

2.144

$x = 3, x = 3,$ $x = \frac{1}{9} x = \frac{1}{9}$

Show solution

2.145

The solution is negative 9 is less than x which is less than 9. The number line shows open circles at negative 9 and 9 with shading in between the circles. The interval notation is negative 9 to 9 within parentheses.

Show solution

2.146

The solution is negative 1 is less than x which is less than 1. The number line shows open circles at negative 1 and 1 with shading in between the circles. The interval notation is negative 1 to 1 within parentheses.

Show solution

2.147

The solution is negative 2 is less than or equal to x which is less than or equal to 3. The number line shows closed circles at negative 2 and 3 with shading between the circles. The interval notation is negative 2 to 3 within brackets.

Show solution

2.148

The solution is one-half is less than or equal to x which is less than or equal to 2. The number line shows closed circles at one-half and 2 with shading between the circles. The interval notation is one-half to 2 within brackets.

Show solution

2.149

The solution is x is less than negative 2 or x is greater than 2. The number line shows an open circle at negative 2 with shading to its left and an open circle at 2 with shading to its right. The interval notation is the union of negative infinity to negative 2 within parentheses and 2 to infinity within parentheses.

Show solution

2.150

The solution is x is less than negative 1 or x is greater than 1. The number line shows an open circle at negative 1 with shading to its left and an open circle at 1 with shading to its right. The interval notation is the union of negative infinity to negative 1 within parentheses and 1 to infinity within parentheses.

Show solution

2.151

The solution is x is less than or equal to negative one-half or x is greater than or equal 2. The number line shows a closed circle at negative one-half with shading to its left and a closed circle at 2 with shading to its right. The interval notation is the union of negative infinity to negative one-half within a parenthesis and a bracket and 2 to infinity within a bracket and a parenthesis

Show solution

2.152

The solution is x is less than or equal to two-thirds or x is greater than or equal 2. The number line shows a closed circle at two-thirds with shading to its left and a closed circle at 2 with shading to its right. The interval notation is the union of negative infinity to two-thirds within a parenthesis and a bracket and 2 to infinity within a bracket and a parenthesis.

Show solution

2.153

The diameter of the rod can be between 79.991 and 80.009 mm.

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2.154

The diameter of the rod can be between 74.95 and 75.05 mm.

Section 2.1 Exercises

Show solution

ⓐ yes ⓑ no

Show solution

ⓐ no ⓑ yes

Show solution

$y = 5 y = 5$

Show solution

$w = −18 w = −18$

Show solution

$q = 3 q = 3$

Show solution

11.

$x = 14 x = 14$

Show solution

13.

$c = 4 c = 4$

Show solution

15.

$c = \frac{5}{2} c = \frac{5}{2}$

Show solution

17.

$n = 2 n = 2$

Show solution

19.

$y = −5 y = −5$

Show solution

21.

$s = 10 s = 10$

Show solution

23.

$p = −4 p = −4$

Show solution

25.

$c = −4 c = −4$

Show solution

27.

$h = \frac{3}{4} h = \frac{3}{4}$

Show solution

29.

$m = 6 m = 6$

Show solution

31.

identity; all real numbers

Show solution

33.

conditional equation; $j = \frac{2}{5} j = \frac{2}{5}$

Show solution

35.

conditional equation; $m = \frac{16}{5} m = \frac{16}{5}$

Show solution

37.

contradiction; no solution

Show solution

39.

contradiction; no solution

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41.

identity; all real numbers

Show solution

43.

$x = −1 x = −1$

Show solution

45.

$y = −1 y = −1$

Show solution

47.

$a = \frac{3}{4} a = \frac{3}{4}$

Show solution

49.

$x = 4 x = 4$

Show solution

51.

$w = \frac{9}{4} w = \frac{9}{4}$

Show solution

53.

$b = 12 b = 12$

Show solution

55.

$p = −41 p = −41$

Show solution

57.

$x = - \frac{5}{2} x = - \frac{5}{2}$

Show solution

59.

$n = −3 n = −3$

Show solution

61.

$x = −2 x = −2$

Show solution

63.

$u = 3 u = 3$

Show solution

65.

$x = 18 x = 18$

Show solution

67.

$x = 20 x = 20$

Show solution

69.

$n = 9 n = 9$

Show solution

71.

$d = 8 d = 8$

Show solution

73.

$L = 19.75 L = 19.75$ feet

Show solution

75.

Answers will vary.

Show solution

77.

Answers will vary.

Show solution

79.

Answers will vary.

Section 2.2 Exercises

Show solution

81.

Answers will vary.

Show solution

83.

six boys

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85.

58 hardback books

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87.

Show solution

89.

Show solution

91.

Show solution

93.

$−5 −5$

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95.

18, 24

Show solution

97.

8, 12

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99.

32, 46

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101.

4, 10

Show solution

103.

38, 39

Show solution

105.

25, 26, 27

Show solution

107.

$−11, −12, −13 −11, −12, −13$

Show solution

109.

84, 86, 88

Show solution

111.

$−69, −71, −73 −69, −71, −73$

Show solution

113.

$750

Show solution

115.

$13,500

Show solution

117.

ⓐ 54 ⓑ 108 ⓐ 30%

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119.

ⓐ $162.5 162.5$ ⓑ $35 ⓐ 150%

Show solution

121.

$$ 11.88 $ 11.88$

Show solution

123.

24.2 g

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125.

2407 mg

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127.

45%

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129.

25%

Show solution

131.

12%

Show solution

133.

200%

Show solution

135.

$−2.5 % −2.5 %$

Show solution

137.

$−11 % −11 %$

Show solution

139.

ⓐ $$ 26.97 $ 26.97$ ⓑ $$ 17.98 $ 17.98$

Show solution

141.

ⓐ $576 ⓑ 30%

Show solution

143.

ⓐ $$ 7.20 $ 7.20$ ⓑ $$ 23.20 $ 23.20$

Show solution

145.

ⓐ $$ 0.20 $ 0.20$ ⓑ $$ 0.80 $ 0.80$

Show solution

147.

$116

Show solution

149.

$4836

Show solution

151.

Show solution

153.

$3.75 % 3.75 %$

Show solution

155.

$35,000

Show solution

157.

$3345

Show solution

159.

$17.5 % 17.5 %$

Show solution

161.

Answers will vary.

Show solution

163.

Answers will vary.

Section 2.3 Exercises

Show solution

165.

$d = \frac{C}{π} d = \frac{C}{π}$

Show solution

167.

$L = \frac{V}{W H} L = \frac{V}{W H}$

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169.

$b = \frac{2 A}{h} b = \frac{2 A}{h}$

Show solution

171.

$d_{1} = \frac{2 A}{d_{2}} d_{1} = \frac{2 A}{d_{2}}$

Show solution

173.

$b_{1} = \frac{2 A}{h} - b_{2} b_{1} = \frac{2 A}{h} - b_{2}$

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175.

$a = \frac{2 h - 108 t}{t^{2}} a = \frac{2 h - 108 t}{t^{2}}$

Show solution

177.

$a = 180 - b - c a = 180 - b - c$

Show solution

179.

$p = \frac{2 A - 2 B}{l} p = \frac{2 A - 2 B}{l}$

Show solution

181.

$L = \frac{P - 2 W}{2} L = \frac{P - 2 W}{2}$

Show solution

183.

$y = 15 - 8 x y = 15 - 8 x$

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185.

$y = −6 + 4 x y = −6 + 4 x$

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187.

$y = 4 + x y = 4 + x$

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189.

$y = \frac{7 - 4 x}{3} y = \frac{7 - 4 x}{3}$

Show solution

191.

$y = \frac{12 - 2 x}{3} y = \frac{12 - 2 x}{3}$

Show solution

193.

$y = \frac{18 - 3 x}{−2} y = \frac{18 - 3 x}{−2}$

Show solution

195.

1 foot

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197.

23 inches

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199.

$45 °, 45 °, 90 ° 45 °, 45 °, 90 °$

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201.

$30 °, 60 °, 90 ° 30 °, 60 °, 90 °$

Show solution

203.

Show solution

205.

Show solution

207.

Show solution

209.

Show solution

211.

$10.2 10.2$

Show solution

213.

$9.8 9.8$

Show solution

215.

18 meters, 11 meters

Show solution

217.

$13.5 13.5$ m, $12.8 12.8$ m

Show solution

219.

25 ft, 50 ft

Show solution

221.

7 m, 11 m

Show solution

223.

12 ft, 13 ft, 14 ft

Show solution

225.

3 ft, 6 ft, 8 ft

Show solution

227.

120 yd, 160 yd

Show solution

229.

40 ft, 85 ft

Show solution

231.

5 feet

Show solution

233.

14.1 feet

Show solution

235.

$104 ° F 104 °$

Show solution

237.

24 ft

Show solution

239.

Answers will vary.

Show solution

241.

ⓐ Answers will vary. ⓑ The areas are the same. The $2 \times 8 2$ rectangle has a larger perimeter than the $4 \times 4 4$ square.
ⓒ Answers will vary.

Section 2.4 Exercises

Show solution

243.

nine nickels, 16 dimes

Show solution

245.

ten $10 bills, five $5 bills

Show solution

247.

63 dimes, 20 quarters

Show solution

249.

16 nickels, 12 dimes, seven quarters

Show solution

251.

330 day passes, 367 tournament passes

Show solution

253.

40 postcards, 100 stamps

Show solution

255.

15 $10 shares, five $12 shares

Show solution

257.

34 general, 61 youth

Show solution

259.

114 general, 246 student

Show solution

261.

Four pounds of macadamia nuts, eight pounds almonds

Show solution

263.

$3.6 3.6$ lbs Bermuda seed, $5.4 5.4$ lbs Fescue seed

Show solution

265.

$33,000 in Fund A, $22,000 in Fund B

Show solution

267.

$5.9 % 5.9 %$

Show solution

269.

Kathy 5 mph, Cheryl 3 mph

Show solution

271.

commercial 540 mph, private plane 330 mph

Show solution

273.

Violet 65 mph, Charlie 55 mph

Show solution

275.

Ethan 22 mph, Leo 16 mph

Show solution

277.

DaMarcus 16 mph, Fabian 22 mph

Show solution

279.

four hours

Show solution

281.

4.5 hours

Show solution

283.

uphill $1.6 1.6$ mph, downhill $4.8 4.8$ mph

Show solution

285.

light traffic 54 mph, heavy traffic 30 mph

Show solution

287.

freeway 72 mph, mountain road 24 mph

Show solution

289.

running eight mph, walking three mph

Show solution

291.

ⓐ 15 minutes ⓑ 20 minutes ⓒ one hour (d) 1:25

Show solution

293.

Answers will vary.

Show solution

295.

Answers will vary.

Section 2.5 Exercises

Show solution

297.

ⓐ

ⓑ

ⓒ

The solution for x is greater than or equal to one-third on a number line has a left bracket at one-third with shading to the right. The solution in interval notation is one-third to infinity within a bracket and a parenthesis.

Show solution

299.

ⓐ

ⓑ

ⓒ

The solution for x is less than negative seven-thirds on a number line has a right parenthesis with shading to the left. The solution in interval notation is negative infinity to negative seven-thirds within parentheses.

Show solution

301.

ⓐ

Negative 2 is less than x which is less than 0. There is an open circle at negative 2 and an open circle at 0 and shading between negative 2 and 0 on the number line. The interval notation is negative 2 and 0 within parentheses.

ⓑ

Negative 5 is less than or equal to x which is less than negative 3. There is a closed circle at negative 5 and an open circle at negative 3 and shading between negative 5 and negative 3 on the number line. The interval notation is negative 5 and negative 3 within a bracket and a parenthesis.

ⓒ

0 is less than or equal to x which is less than or equal to 3.5. There is a closed circle at 0 and a closed circle at 3.5 and shading between 0 and 3.5 on the number line. The interval notation is 0 and 3.5 within brackets.

Show solution

303.

ⓐ

Negative 4 is less than x which is less than 2. There is a open circle at negative 4 and an open circle at 2 and shading between negative 4 and 2 on the number line. The interval notation is negative 4 and 2 within parentheses.

ⓑ

Negative 5 is less than x which is less than or equal to 2. There is a open circle at negative 5 and a closed circle at negative 2 and shading between negative 5 and negative 2 on the number line. The interval notation is negative 5 and negative 2 within a parenthesis and a bracket.

ⓒ

Negative 3.75 is less than or equal to x which is less than or equal to 0. There is a closed circle at negative 3.75 and a closed circle at 0 and shading between negative 3.75 and 0 on the number line. The interval notation is negative 3.75 and 0 within brackets.

Show solution

305.

ⓐ

The solution is b is greater than or equal to negative seventeen twenty-fourths. The solution on a number line has a left bracket negative seventeen twenty-fourths with shading to the right. The solution in interval notation is negative seventeen twenty-fourths to infinity within a bracket and a parenthesis.

ⓑ

The solution is y is less than 8. The solution on a number line has a right parenthesis at 8 with shading to the left. The solution in interval notation is negative infinity to 8 within parentheses.

ⓒ

The solution is k is greater than 64. The solution on a number line has a left parenthesis at 64 with shading to the right. The solution in interval notation is 64 to infinity within parentheses.

Show solution

307.

ⓐ

The solution is g is less than twenty-three thirty-sixths. The solution on a number line has a right parenthesis at twenty-three thirty-sixths with shading to the left. The solution in interval notation is negative infinity to twenty-three thirty-sixths within parentheses.

ⓑ

The solution is s is less than negative 4. The solution on a number line has a right parenthesis at negative 4 with shading to the left. The solution in interval notation is negative infinity to negative 4 within parentheses.

ⓒ

The solution is g is less than or equal to 16. The solution on a number line has a right bracket at 16 with shading to the left. The solution in interval notation is negative infinity to 16 within parenthesis and a bracket.

Show solution

309.

ⓐ

The solution is v is greater than or equal to negative 12. The solution on a number line has a left bracket with shading to the right. The solution in interval notation is negative 12 to infinity within a bracket and a parenthesis.

ⓑ

The solution is b is less than or equal to negative 300. The solution on a number line has a right bracket at negative 300 with shading to the left. The solution in interval notation is negative infinity to negative 300 within a parenthesis and a bracket.

Show solution

311.

ⓐ

The solution is d is less than negative 15. The solution on a number line has a right parentheses with shading to the left. The solution in interval notation is negative infinity to negative 15 within parentheses.

ⓑ

The solution is q is greater than 108. The solution on a number line has a left parentheses at 108 with shading to the right. The solution in interval notation is 108 to infinity within parentheses.

Show solution

313.

The solution is u is greater than or equal to 7. The solution on a number line has a left bracket at 7 with shading to the right. The solution in interval notation is 7 to infinity within a a bracket and a parenthesis.

Show solution

315.

The solution is p is less than eighteen fifths. The solution on a number line has a right parenthesis at eighteen fifths with shading to the left. The solution in interval notation negative infinity to eighteen fifths within parentheses.

Show solution

317.

The solution is y is less than negative 5. The solution on a number line has a right parenthesis at negative 5 with shading to the left. The solution in interval notation is negative infinity to negative 5 within parentheses.

Show solution

319.

The solution is k is less than or equal to 7. The solution on a number line has a right bracket at 7with shading to the left. The solution in interval notation is negative infinity to 7 within a parenthesis and a bracket.

Show solution

321.

Show solution

323.

Show solution

325.

Show solution

327.

Show solution

329.

The solution is k is greater than or equal to negative eleven fifthss. The solution on a number line has a left bracket at negative eleven fifths with shading to the right. The solution in interval notation is negative eleven fifths to negative infinity within a bracket and a parenthesis.

Show solution

331.

Show solution

333.

The solution is y is greater than or equal to ten twenty-ninths. The solution on a number line has a left bracket at ten twenty-ninths with shading to the right. The solution in interval notation is ten twenty-ninths to infinity within a bracket and a parenthesis.

Show solution

335.

The solution is g is greater than negative 90. The solution on a number line has a left parenthesis at negative 90 with shading to the right. The solution in interval notation is negative 90 to infinity within parentheses.

Show solution

337.

The solution is n is less than or equal to negative 78. The solution on a number line has a right bracket at negative 78 with shading to the left. The solution in interval notation is negative infinity to negative 78 within a parenthesis and a bracket.

Show solution

339.

The inequality is k plus 6 is greater than 25. Its solution is k is greater than 19. The solution on a number line has a left parenthesis at 19 with shading to the right. The solution in interval notation is 19 to infinity within parentheses.

Show solution

341.

The inequality is x minus 12 is greater than or equal to 21. Its solution is x is greater than or equal to 33. The solution on a number line has a left bracket at 33 with shading to the right. The solution in interval notation is 33 to infinity within a bracket and a parenthesis.

Show solution

343.

The inequality is negative 2 s is less than 56. Its solution is s is greater than negative 28. The solution on a number line has a left parenthesis at negative 28 with shading to the right. The solution in interval notation is negative 28 to infinity within parentheses.

Show solution

345.

The inequality is a minus 15 is greater than or equal to negative 7. Its solution is a is greater than or equal to 8. The solution on a number line has a left bracket at 8 with shading to the right. The solution in interval notation is 8 to infinity within a bracket and a parenthesis.

Show solution

347.

A maximum of 14 people can safely ride in the elevator.

Show solution

349.

five drinks

Show solution

351.

86 cars

Show solution

353.

$16,875

Show solution

355.

$110,000

Show solution

357.

260 messages

Show solution

359.

35 people

Show solution

361.

32 jobs

Show solution

363.

62 necklaces

Show solution

365.

seven lawns

Show solution

367.

20 hours

Show solution

369.

20 people

Show solution

371.

42 guests

Show solution

373.

Answers will vary.

Show solution

375.

Answers will vary.

Section 2.6 Exercises

Show solution

377.

The solution is negative 2 is less than x which is less than or equal to 4. Its graph has an open circle at 1negative 2 and a closed circle at 4 with shading between the open and closed circles. Its interval notation is negative 2 to 4 within a parenthesis and a bracket.

Show solution

379.

The solution is negative 6 is less than x which is less than negative 3. Its graph has an open circle at negative 6 and an open circle at negative 3 with shading between open circles. Its interval notation is negative 6 to negative 3 within parentheses.

Show solution

381.

The solution is negative 2 is less than or equal to x which is less than 2. Its graph has a closed circle at negative 2 and an open circle at 2 with shading between the closed and open circles. Its interval notation is negative 2 to 2 within a bracket and a parenthesis.

Show solution

383.

The solution is negative 1 is less than x which is less than or equal to three-halves. Its graph has an open circle at negative 1 and a closed circle at three-halves with shading between the open and closed circles. Its interval notation is negative 1 to three-halves within a parenthesis and a bracket.

Show solution

385.

The solution is negative 2 is less than x which is less than 2. Its graph has an open circle at negative 2 and an open circle at 2 with shading between the open circles. Its interval notation is negative 2 to 2 within parentheses.

Show solution

387.

The solution is x is less than negative 2. Its graph has an open circle at negative 2 and is shaded to the left. Its interval notation is negative infinity to negative 2 within parentheses.

Show solution

389.

The solution is x is greater than or equal to negative 2. Its graph has a closed circle at negative 2 and is shaded to the right. Its interval notation is negative 2 to infinity within a bracket and a parenthesis.

Show solution

391.

The solution is x is less than or equal to 12. Its graph has a closed circle at 12 and is shaded to the left. Its interval notation is negative infinity to 12 within a parenthesis and a bracket.

Show solution

393.

The solution is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.

Show solution

395.

Show solution

397.

The solution is 1 is less than x which is less than or equal to 3. Its graph has an open circle at 1 and a closed circle at 3 and is shaded between the open and closed circles. Its interval notation is 1 to 3 within a parenthesis and a bracket.

Show solution

399.

The solution is negative 1 is less than x which is less than 2. Its graph has an open circle at negative 1 an open circle at 2 and is shaded between. Its interval notation is negative 1 to 2 within parentheses.

Show solution

401.

The solution is negative 1 is less than or equal to x which is less than or 0. Its graph has a closed circle at negative 1 and an open circle at 0 and is shaded between the closed and open circles. Its interval notation is negative 1 to 0 within a bracket and a parenthesis.

Show solution

403.

The solution is x is less than or equal to negative 4 or x is greater than negative 3. The graph of the solutions on a number line has a closed circle at negative 4 and shading to the left and an open circle at negative 3 with shading to the right. The interval notation is the union of negative infinity to negative 4 within a parenthesis and a bracket and negative 3 and infinity within parentheses.

Show solution

405.

The solution is x is less than 0 or x is greater than or equal to 2. The graph of the solutions on a number line has an open circle at 0 and shading to the left and a closed circle at 4 with shading to the right. The interval notation is the union of negative infinity to 0 within parentheses and 4 to infinity within a bracket and parenthesis.

Show solution

407.

The solution is x is less than or equal to negative 2 or x is greater than or equal to 2. The graph of the solutions on a number line has a closed circle at negative 2 and shading to the left and a closed circle at 2 with shading to the right. The interval notation is the union of negative infinity to negative 2 within a parenthesis and a bracket and 2 to infinity within a bracket and a parenthesis.

Show solution

409.

The solution is x is less than two-thirds or x is greater than 1. The graph of the solutions on a number line has an open circle at two-thirds and shading to the left and an open circle at 1 with shading to the right. The interval notation is the union of negative infinity to two-thirds within parentheses and 1 and infinity within parentheses.

Show solution

411.

The solution is x is less than 3 or x is greater than 12. The graph of the solutions on a number line has an open circle at 3 and shading to the left and an open circle at 12 with shading to the right. The interval notation is the union of negative infinity to 3 within parentheses and 12 and infinity within parentheses.

Show solution

413.

Show solution

415.

Show solution

417.

The solution is x is less than 1. Its graph has an open circle at negative 1 is shaded to the right. Its interval notation is 1 to infinity within parentheses.

Show solution

419.

Show solution

421.

Show solution

423.

The solution is negative 1 is less than x which is less than or equal to two-thirds. Its graph has an open circle at negative 1 and a closed circle at two-thirds and is shaded between the open and closed circles. Its interval notation is negative 1 to two-thirds within a parenthesis and a bracket.

Show solution

425.

The solution is negative 1 is less than or equal to x which is less than 2. Its graph has a closed circle at negative 1 and a closed circle at 2 and is shaded between the closed circles. Its interval notation is negative 1 to 4 within brackets.

Show solution

427.

$5 \leq n \leq 24 5 \leq n \leq 24$

Show solution

429.

$6 \leq w \leq 12 6 \leq w \leq 12$

Show solution

431.

ⓐ answers vary ⓑ answers vary

Show solution

433.

Answers will vary.

Section 2.7 Exercises

Show solution

435.

Show solution

437.

Show solution

439.

$x = 1, x = - \frac{1}{2} x = 1, x = - \frac{1}{2}$

Show solution

441.

$x = −1, x = - \frac{5}{2} x = −1, x = - \frac{5}{2}$

Show solution

443.

$x = 7, x = 1 x = 7, x = 1$

Show solution

445.

$x = 1, x = −5 x = 1, x = −5$

Show solution

447.

$x = 7, x = 1 x = 7, x = 1$

Show solution

449.

no solution

Show solution

451.

no solution

Show solution

453.

$x = −1, x = - \frac{2}{3} x = −1, x = - \frac{2}{3}$

Show solution

455.

$x = −3, x = 3 x = −3, x = 3$

Show solution

457.

The solution is negative 1 is less than x which is less than 1. The number line shows an open circle at negative 1, an open circle at 1, and shading between the circles. The interval notation is negative 1 to 1 within parentheses.

Show solution

459.

The solution is negative 3 is less than or equal to x which is less than or equal to 3. The number line shows a closed circle at negative 3, a closed circle at 3, and shading between the circles. The interval notation is negative 3 to 3 within brackets.

Show solution

461.

The solution is 1 is less than or equal to x which is less than or equal to 4. The number line shows a closed circle at 1, a closed circle at 4, and shading between the circles. The interval notation is 1 to 4 within brackets.

Show solution

463.

Show solution

465.

The solution is negative one-third is less than x which is less than 2. The number line shows an open circle at negative one-half, an open circle at 2, and shading between the circles. The interval notation is negative one-third to 2 within parentheses.

Show solution

467.

Show solution

469.

The solution is x is less than negative 6 or x is greater than 6. The number line shows an open circle at negative 6 with shading to its left and an open circle at 6 with shading to its right. The interval notation is the union of negative infinity to negative 6 within parentheses and 6 to infinity within parentheses

Show solution

471.

The solution is x is less than negative 5 or x is greater than 5. The number line shows an open circle at negative 5 with shading to its left and an open circle at 5 with shading to its right. The interval notation is the union of negative infinity to negative 5 within parentheses and 5 to infinity within parentheses.

Show solution

473.

Show solution

475.

The solution is x is less than negative 2 or x is greater than 3. The number line shows an open circle at negative 2 with shading to its left and an open circle at 3 with shading to its right. The interval notation is the union of negative infinity to negative 2 within parentheses and 3 to infinity within parentheses.

Show solution

477.

The solution is x is less than or equal to 6 or x is greater than or equal to 8. The number line shows a closed circle at 6 with shading to its left and a closed circle at 8 with shading to its right. The interval notation is the union of negative infinity to 6 within parenthesis and a bracket and 8 to infinity within a bracket and a parenthesis.

Show solution

479.

Show solution

481.

$x = 4, x = \frac{2}{7} x = 4, x = \frac{2}{7}$

Show solution

483.

$x = 3, x = 2 x = 3, x = 2$

Show solution

485.

$x = 3, x = - \frac{11}{3} x = 3, x = - \frac{11}{3}$

Show solution

487.

$x = \frac{3}{2}, x = - \frac{1}{2} x = \frac{3}{2}, x = - \frac{1}{2}$

Show solution

489.

Show solution

491.

The minimum to maximum expected production is 207,500 to 2,225,000 bottles

Show solution

493.

The acceptable weight is 22.5 to 25.5 ounces.

Show solution

495.

Answers will vary.

Review Exercises

Show solution

497.

Show solution

499.

$s = −22 s = −22$

Show solution

501.

$m = −14 m = −14$

Show solution

503.

$q = 18 q = 18$

Show solution

505.

$x = −1 x = −1$

Show solution

507.

$k = \frac{3}{4} k = \frac{3}{4}$

Show solution

509.

contradiction; no solution

Show solution

511.

$n = 2 n = 2$

Show solution

513.

$k = 23 k = 23$

Show solution

515.

$x = 5 x = 5$

Show solution

517.

There are 116 people.

Show solution

519.

Show solution

521.

$−3, −10 −3, −10$

Show solution

523.

76, 78, 80

Show solution

525.

$922

Show solution

527.

160

Show solution

529.

$$ 3.89 $ 3.89$

Show solution

531.

35%

Show solution

533.

32%

Show solution

535.

ⓐ $105 ⓑ $52.5 % 52.5 %$

Show solution

537.

$428.22

Show solution

539.

$1,900

Show solution

541.

$d_{2} = \frac{2 A}{d_{1}} d_{2} = \frac{2 A}{d_{1}}$

Show solution

543.

$y = \frac{4 x}{3} - 4 y = \frac{4 x}{3} - 4$

Show solution

545.

$22.5 °, 67.5 °, 90 ° 22.5 °,$

Show solution

547.

Show solution

549.

6 feet

Show solution

551.

$24.5 24.5$ cm, $12.5 12.5$ cm

Show solution

553.

9 ft, 14 ft, 12 ft

Show solution

555.

nine pennies, six dimes, 12 quarters

Show solution

557.

57 students, 68 adults

Show solution

559.

$2.2 2.2$ lbs of raisins, $7.8 7.8$ lbs of nuts

Show solution

561.

$9.7 % 9.7 %$

Show solution

563.

Louellen 65 mph, Tracy 66 mph

Show solution

565.

upstream 3 mph, downstream 5 mph

Show solution

567.

heavy traffic 32 mph, light traffic 66 mph

Show solution

569.

The solution is x is greater than or equal to negative 2.5. The number line shows a left bracket at negative 2.5 with shading to its right. The interval notation is negative 2.5 to infinity within a bracket and a parenthesis.

Show solution

571.

Show solution

573.

The solution is negative 5 is less than or equal to x which is less than negative 3. The number line shows a closed circle at negative 5, an open circle at negative 3, and shading between the circles. The interval notation is negative 5 to negative 3 within a bracket and a parenthesis.

Show solution

575.

The solution is n is less than or equal to 35. The number line shows a a right bracket at 35 with shading to its left. The interval notation is negative infinity to 35 within a parenthesis and a bracket.

Show solution

577.

The solution is x is greater than 6. The number line shows a left parenthesis at 6 with shading to its right. The interval notation is 6 to infinity within parentheses.

Show solution

579.

The solution is p is less than ten-thirds. The number line shows a right parenthesis at ten-thirds with shading to its left. The interval notation is negative infinity to ten-thirds within parentheses.

Show solution

581.

Show solution

583.

The inequality is z plus 5 is less than or equal to 19. Its solution is z is less than or equal to 14. The number line shows a right bracket at 14 with shading to its left. The interval notation is negative infinity to 14 within a parenthesis and a bracket.

Show solution

585.

The inequality is 9 n is greater than 42. Its solution is n is greater than fourteen-thirds. The number line shows a left parentheses at fourteen-thirds with shading to its right. The interval notation is fourteen-thirds to infinity within parentheses.

Show solution

587.

$33 per day

Show solution

589.

at least $300,000

Show solution

591.

at least 112 jobs

Show solution

593.

The solution is negative 3 is less than x which is less than or equal to 5. The number line shows an open circle at negative 3 and a closed circle at 5. The interval notation is negative 3 to 5 within a parenthesis and a bracket.

Show solution

595.

The solution is negative x is less than negative five-fourths. The number line shows an open circle at negative five-fourths with shading to its left. The interval notation is negative infinity to negative five-fourths within parentheses.

Show solution

597.

The solution is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation

Show solution

599.

The solution is x is less than negative two-thirds or x is greater than or equal to 3. The number line shows a closed circle at negative two-thirds with shading to its left and a closed circle at 3 with shading to its right. The interval notation is the union of negative infinity to negative two-thirds within a parenthesis and a bracket and 3 to infinity within a bracket and a parenthesis.

Show solution

601.

The solution is x is less than 2 or x is greater than 8. The number line shows an open circle at 2 with shading to its left and an open circle at 8 with shading to its right. The interval notation is the union of negative infinity to 8 within parentheses and 8 to infinity within parentheses.

Show solution

603.

Show solution

605.

$6 \leq w \leq 12 6 \leq w \leq 12$

Show solution

607.

no solution

Show solution

609.

$x = 2, x = \frac{2}{3} x = 2, x = \frac{2}{3}$

Show solution

611.

$x = 9, x = −3 x = 9, x = −3$

Show solution

613.

$x = 2, x = \frac{1}{4} x = 2, x = \frac{1}{4}$

Show solution

615.

The solution is 1 is less than or equal to x which is less than or equal to 4. The number line shows a closed circle at 1, a closed circle at 4, and shading in between the circles. The interval notation is 1 to 4 within brackets.

Show solution

617.

Show solution

619.

The solution is x is less than negative 2 or x is greater than 6. The number line shows a closed circle at negative 2 with shading to its left and a closed circle at 2 with shading to its right. The interval notation is the union of negative infinity to negative 2 within a parenthesis and a bracket and 2 to infinity within a bracket and a parenthesis.

Show solution

621.

Show solution

623.

The minimum to maximum expected usage is 210,000 to 220,000 bottles

Practice Test

Show solution

625.

$x = −5 x = −5$

Show solution

627.

$a = 41 a = 41$

Show solution

629.

contradiction; no solution

Show solution

631.

$x = 6 x = 6$

Show solution

633.

$x = −2, x = - \frac{1}{3} x = −2, x = - \frac{1}{3}$

Show solution

635.

Show solution

637.

Show solution

639.

The solution is c is greater than one-third. The number line shows a left parenthesis at one-third with shading to its right. The interval notation is one-third to infinity within parentheses.

Show solution

641.

The solution is x is less than two-thirds or x is greater than 1. The number line shows an open circle at two-thirds with shading to its left and an open circle at 1 with shading to its right. The interval notation is the union of negative infinity to two-thirds within parentheses and 1 to infinity within parentheses.

Show solution

643.

The solution is x is less than or equal to negative one-half or x is greater than or equal to 2. The number line shows a closed circle at negative one-half with shading to its left and a closed circle at 2 with shading to its right. The interval notation is the union of negative infinity to negative one-half within a parenthesis and bracket and 2 to infinity within a bracket and a parenthesis.

Show solution

645.

$10.8 10.8$

Show solution

647.

$−57, −55 −57, −55$

Show solution

649.

12 dimes, seven quarters

Show solution

651.

$30 °, 60 °, 90 ° 30 °, 60 °, 90 °$

Show solution

653.

$2.5 2.5$ hours

Show solution

655.

At most $55.56 per costume.