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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Be Prepared

2.1

18x+3018x+30

2.2

32n32n

2.3

1212

2.4

2x62x6

2.5

0.0450.045

2.6

60%60%

2.7

1616

2.8

w23ww23w

2.9

6363

2.10

x=6x=6

2.11

2c+32c+3

2.12

0.00420.0042

2.13

1212 is greater than xx.

2.14

x15x15

2.15

25x+425x+4

2.16

x+4x+4

2.17

77

2.18

a. >; b. >; c. >; d. >

2.19

1212

Try It

2.1

no yes

2.2

yes no

2.3

m=2m=2

2.4

a=0a=0

2.5

u=2u=2

2.6

x=4x=4

2.7

p=−2p=−2

2.8

q=−8q=−8

2.9

y=175y=175

2.10

z=0z=0

2.11

identity; all real numbers

2.12

identity; all real numbers

2.13

conditional equation; q=911q=911

2.14

conditional equation; k=20114k=20114

2.15

contradiction; no solution

2.16

contradiction; no solution

2.17

x=12x=12

2.18

x=−2x=−2

2.19

x=12x=12

2.20

u=−12u=−12

2.21

n=2n=2

2.22

m=−1m=−1

2.23

r=1r=1

2.24

s=−8s=−8

2.25

n=9n=9

2.26

d=16d=16

2.27

He bought two notebooks.

2.28

He did seven crosswords puzzles.

2.29

33

2.30

66

2.31

−15,−8−15,−8

2.32

−29,11−29,11

2.33

−33,−32,−31−33,−32,−31

2.34

−13,−12,−11−13,−12,−11

2.35

32, 34, 36

2.36

−10,−8,−6−10,−8,−6

2.37

The average cost was $5,000.

2.38

The median price was $19,300.

2.39

36 $26 125%125%

2.40

33 $36 175%175%

2.41

25 grams

2.42

2,375 mg

2.43

50%

2.44

40%

2.45

8.8%8.8%

2.46

50%

2.47

$600 $1,800

2.48

$2,975 $11,475

2.49

He will earn $2,500.

2.50

She earned $7,020.

2.51

The rate of simple interest was 6%.

2.52

The rate of simple interest was 5.5%.

2.53

He paid $17,590.

2.54

She deposited $9,600.

2.55

b=2Ahb=2Ah

2.56

h=2Abh=2Ab

2.57

C=59(F32)C=59(F32)

2.58

b=2ABhhb=2ABhh

2.59

t=APPrt=APPr

2.60

r=APPtr=APPt

2.61

y=94x7y=94x7

2.62

y=15x8y=15x8

2.63

The window’s height is 12 meters.

2.64

The length of the base is 6 feet.

2.65

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

2.66

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

2.67

The length of the leg is 8.

2.68

The length of the leg is 12.

2.69

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

2.70

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

2.71

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

2.72

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

2.73

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

2.74

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

2.75

The ladder reaches 12 feet.

2.76

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

2.77

Jess has 41 nickels and 18 quarters.

2.78

Elane has 22 nickels and 59 dimes.

2.79

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

2.80

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

2.81

84 adult tickets, 31 student tickets

2.82

615 children’s tickets and 195 adult tickets

2.83

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

2.84

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

2.85

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

2.86

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

2.87

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

2.88

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

2.89

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

2.90

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

2.91

Suzy’s speed uphill is 1.81.8 mph and downhill is three mph.

2.92

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

2.93

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

2.94

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

2.95


The graph of the inequality x is greater than 2 is indicated on a number line with a left parenthesis at 2 and shading to the right. The solution in interval notation is the interval from 2 to infinity enclosed within parentheses.


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.
2.96


The graph of the inequality x is less than or equal to negative 4 is indicated on a number line with a right bracket at negative 4 and shading to the left. The solution in interval notation is the interval from negative infinity to negative 4 enclosed within an left parenthesis and right bracket.


The graph of the inequality x is greater than or equal to 0.5 is indicated on a number line with a left bracket at 0.5 and shading to the right. The solution in interval notation is the interval from 0.5 to infinity enclosed within a left bracket and right parenthesis.


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.
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.
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.
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.
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.
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.
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.
2.113

Angie can buy 7 packs of juice.

2.114

Daniel can have 11 people at the party.

2.115

Sergio and Lizeth can travel no more than 500 miles.

2.116

Rameen can use no more than 76 therms.

2.117

Caleb must work at least 96 hours.

2.118

Elliot must work at least 85 jobs.

2.119

Brenda must babysit at least 27 hours.

2.120

Josue must shovel at least 20 driveways.

2.133

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

2.134

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

2.135

±2±2 no solution 0

2.136

±11±11 no solution 0

2.137

x=4,x=23x=4,x=23

2.138

x=−1,x=52x=−1,x=52

2.139

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

2.140

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

2.141

No solution

2.142

No solution

2.143

x=25,x=25, x=52x=52

2.144

x=3,x=3, x=19x=19

2.153

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

2.154

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

Section 2.1 Exercises

1.

yes no

3.

no yes

5.

y=5y=5

7.

w=−18w=−18

9.

q=3q=3

11.

x=14x=14

13.

c=4c=4

15.

c=52c=52

17.

n=2n=2

19.

y=−5y=−5

21.

s=10s=10

23.

p=−4p=−4

25.

c=−4c=−4

27.

h=34h=34

29.

m=6m=6

31.

identity; all real numbers

33.

conditional equation;j=25j=25

35.

conditional equation; m=165m=165

37.

contradiction; no solution

39.

contradiction; no solution

41.

identity; all real numbers

43.

x=−1x=−1

45.

y=−1y=−1

47.

a=34a=34

49.

x=4x=4

51.

w=94w=94

53.

b=12b=12

55.

p=−41p=−41

57.

x=52x=52

59.

n=−3n=−3

61.

x=−2x=−2

63.

u=3u=3

65.

x=18x=18

67.

x=20x=20

69.

n=9n=9

71.

d=8d=8

73.

L=19.75L=19.75 feet

75.

Answers will vary.

77.

Answers will vary.

79.

Answers will vary.

Section 2.2 Exercises

81.

Answers will vary.

83.

six boys

85.

58 hardback books

87.

15

89.

5

91.

12

93.

−5−5

95.

18, 24

97.

8, 12

99.

32, 46

101.

4, 10

103.

38, 39

105.

25, 26, 27

107.

−11,−12,−13−11,−12,−13

109.

84, 86, 88

111.

−69,−71,−73−69,−71,−73

113.

$750

115.

$13,500

117.

54 108 30%

119.

162.5162.5 $35 150%

121.

$11.88$11.88

123.

24.2 g

125.

2407 mg

127.

45%

129.

25%

131.

12%

133.

200%

135.

−2.5%−2.5%

137.

−11%−11%

139.

$26.97$26.97 $17.98$17.98

141.

$576 30%

143.

$7.20$7.20 $23.20$23.20

145.

$0.20$0.20 $0.80$0.80

147.

$116

149.

$4836

151.

3%

153.

3.75%3.75%

155.

$35,000

157.

$3345

159.

17.5%17.5%

161.

Answers will vary.

163.

Answers will vary.

Section 2.3 Exercises

165.

d=Cπd=Cπ

167.

L=VWHL=VWH

169.

b=2Ahb=2Ah

171.

d1=2Ad2d1=2Ad2

173.

b1=2Ahb2b1=2Ahb2

175.

a=2h108tt2a=2h108tt2

177.

a=180bca=180bc

179.

p=2A2Blp=2A2Bl

181.

L=P2W2L=P2W2

183.

y=158xy=158x

185.

y=−6+4xy=−6+4x

187.

y=4+xy=4+x

189.

y=74x3y=74x3

191.

y=122x3y=122x3

193.

y=183x−2y=183x−2

195.

1 foot

197.

23 inches

199.

45°,45°,90°45°,45°,90°

201.

30°,60°,90°30°,60°,90°

203.

15

205.

25

207.

8

209.

12

211.

10.210.2

213.

9.89.8

215.

18 meters, 11 meters

217.

13.513.5 m, 12.812.8 m

219.

25 ft, 50 ft

221.

7 m, 11 m

223.

12 ft, 13 ft, 14 ft

225.

3 ft, 6 ft, 8 ft

227.

120 yd, 160 yd

229.

40 ft, 85 ft

231.

5 feet

233.

14.1 feet

235.

104°F104°F

237.

240 ft

239.

Answers will vary.

241.

Answers will vary. The areas are the same. The 2×82×8 rectangle has a larger perimeter than the 4×44×4 square.
Answers will vary.

Section 2.4 Exercises

243.

nine nickels, 16 dimes

245.

ten $10 bills, five $5 bills

247.

63 dimes, 20 quarters

249.

16 nickels, 12 dimes, seven quarters

251.

330 day passes, 367 tournament passes

253.

40 postcards, 100 stamps

255.

15 $10 shares, five $12 shares

257.

34 general, 61 youth

259.

114 general, 246 student

261.

Four pounds of macadamia nuts, eight pounds almonds

263.

3.63.6 lbs Bermuda seed, 5.45.4 lbs Fescue seed

265.

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

267.

5.9%5.9%

269.

Kathy 5 mph, Cheryl 3 mph

271.

commercial 550 mph, private plane 340 mph

273.

Violet 65 mph, Charlie 55 mph

275.

Ethan 22 mph, Leo 16 mph

277.

DaMarcus 16 mph, Fabian 22 mph

279.

four hours

281.

4.5 hours

283.

uphill 1.61.6 mph, downhill 4.84.8 mph

285.

light traffic 54 mph, heavy traffic 30 mph

287.

freeway 67 mph, mountain road 22.3 mph

289.

running eight mph, walking three mph

291.

15 minutes 20 minutes one hour (d) 1:25

293.

Answers will vary.

295.

Answers will vary.

Section 2.5 Exercises

297.



The solution for x is greater than 3 on a number line has a left bracket 3 with shading to the right. The solution in interval notation is 3 to infinity within parentheses.



The solution for x is less than or equal to negative 0.5 on a number line has a right bracket at negative 0.5 with shading to the left. The solution in interval notation is negative infinity to negative 0.5 within a parenthesis and a bracket.


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.
299.



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



The solution for x is greater than or equal to negative 1.5 on a number line has a left bracket with shading to the right. The solution in interval notation is negative 1.5 to infinity within a bracket and a parenthesis.



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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
321.


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.
323.


The inequality is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation.
325.


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.
327.


The inequality is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation.
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.
331.


The inequality is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation.
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.
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.
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.
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.
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.
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.
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.
347.

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

349.

five drinks

351.

86 cars

353.

$16,875

355.

$110,000

357.

260 messages

359.

35 people

361.

32 jobs

363.

62 necklaces

365.

seven lawns

367.

20 hours

369.

20 people

371.

42 guests

373.

Answers will vary.

375.

Answers will vary.

Section 2.6 Exercises

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.
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.
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.
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.
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.
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.
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.
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.
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.
395.
The solution is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.
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.
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.
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.
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.
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.
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.
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.
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.
413.
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.
415.
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.
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.
419.
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.
421.
The inequality is a contradiction. So, there is no solution. As a result, there is no graph on the number line or interval notation.
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.
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.
427.

5n245n24

429.

6w126w12

431.

answers vary answers vary

433.

Answers will vary.

Section 2.7 Exercises

435.

x=4,x=−4x=4,x=−4 no solution z=0z=0

437.

x=3,x=−3x=3,x=−3 no solution z=0z=0

439.

x=1,x=12x=1,x=12

441.

x=−1,x=52x=−1,x=52

443.

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

445.

x=1,x=−5x=1,x=−5

447.

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

449.

no solution

451.

no solution

453.

x=−1,x=23x=−1,x=23

455.

x=−3,x=3x=−3,x=3

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.
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.
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.
463.
The solution is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.
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.
467.
The solution is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.
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
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.
473.
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.
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.
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.
479.
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.
481.

x=2,x=14x=2,x=14

483.

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

485.

x=3,x=113x=3,x=113

487.

x=32,x=12x=32,x=12

489.
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.
491.

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

493.

The acceptable weight is 22.5 to 25.5 ounces.

495.

Answers will vary.

Review Exercises

497.

no

499.

s=−22s=−22

501.

m=−14m=−14

503.

q=18q=18

505.

x=−1x=−1

507.

k=34k=34

509.

contradiction; no solution

511.

n=2n=2

513.

k=23k=23

515.

x=5x=5

517.

There are 116 people.

519.

38

521.

−3,−10−3,−10

523.

76, 78, 80

525.

$922

527.

160

529.

$3.89$3.89

531.

35%

533.

32%

535.

$105 52.5%52.5%

537.

$428.22

539.

$1,900

541.

d2=2Ad1d2=2Ad1

543.

y=4x34y=4x34

545.

22.5°,67.5°,90°22.5°,67.5°,90°

547.

26

549.

6 feet

551.

24.524.5 cm, 12.512.5 cm

553.

9 ft, 14 ft, 12 ft

555.

nine pennies, six dimes, 12 quarters

557.

57 students, 68 general admission

559.

2.22.2 lbs of raisins, 7.87.8 lbs of nuts

561.

9.7%9.7%

563.

Louellen 65 mph, Tracy 66 mph

565.

upstream 3 mph, downstream 5 mph

567.

heavy traffic 32 mph, light traffic 68 mph

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.
571.
The solution is x is greater than 2. The number line shows a left parenthesis at 2 with shading to its right. The interval notation is 2 to infinity within parentheses.
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.
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.
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.
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.
581.
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.
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.
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.
587.

$33 per day

589.

at least $300,000

591.

at least 112 jobs

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.
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.
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
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.
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.
603.
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.
605.

6w126w12

607.

no solution

609.

x=2,x=23x=2,x=23

611.

x=9,x=−3x=9,x=−3

613.

x=2,x=14x=2,x=14

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.
617.
The solution is a contradiction. So, there is no solution. As a result, there is no graph or the number line or interval notation.
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.
621.
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 negative 6 within a parenthesis and a bracket and 8 to infinity within a bracket and a parenthesis.
623.

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

Practice Test

625.

x=−5x=−5

627.

a=41a=41

629.

contradiction; no solution

631.

x=6x=6

633.

x=−2,x=13x=−2,x=13

635.
The inequality is x is greater than or equal to negative 3.5. The number line shows a left bracket at negative 3.5 and shading to the right. The interval notation is negative 3.5 to infinity within a bracket and a parenthesis.
637.
The inequality is negative two is less than or equal to x which is less than 5. The number line shows a closed circle at negative 2 and an open circle at 5 with shading between the circles. The interval notation is negative 2 to 5 within a bracket and a parenthesis.
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.
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.
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.
645.

10.810.8

647.

−57,−55−57,−55

649.

12 dimes, seven quarters

651.

30°,60°,90°30°,60°,90°

653.

2.52.5 hours

655.

At most $55.56 per costume.

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