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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 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
  13. Index

Be Prepared

2.1

11

2.2

2020

2.3

n+4n+4

2.4

x5x5

2.5

11

2.6

2525

2.7

4y4y

2.8

a+4a+4

2.9

18x+3018x+30

2.10

32n32n

2.11

21y+2721y+27

2.12

1616

2.13

33

2.14

1212

2.15

478478

2.16

88

2.17

1212

2.18

1515 is greater than x.

2.19

n=33n=33

2.20

p=235p=235

2.21

a=2a=2

Try It

2.1

no

2.2

yes

2.3

x=−46x=−46

2.4

x=−50x=−50

2.5

n=−14n=−14

2.6

p=−32p=−32

2.7

p=96=32p=96=32

2.8

q=43q=43

2.9

b=−1.63b=−1.63

2.10

c=−3.67c=−3.67

2.11

y=15y=15

2.12

z=2z=2

2.13

p=5p=5

2.14

q=−16q=−16

2.15

h=6h=6

2.16

x=2x=2

2.17

x+10=41;x=31x+10=41;x=31

2.18

x12=51;x=63x12=51;x=63

2.19

4x3x=14;x=144x3x=14;x=14

2.20

7a6a=−8;a=−87a6a=−8;a=−8

2.21

7 pounds

2.22

42 books

2.23

$20,900

2.24

$11.00

2.25

y=−413y=−413

2.26

z=−554z=−554

2.27

a=294a=294

2.28

b=144b=144

2.29

k=−8k=−8

2.30

g=−3g=−3

2.31

n=35n=35

2.32

y=18y=18

2.33

z=920z=920

2.34

r=516r=516

2.35

c=−3c=−3

2.36

x=47x=47

2.37

q=−6q=−6

2.38

r=−5r=−5

2.39

132=−12y;y=−11132=−12y;y=−11

2.40

117=−13z;z=−9117=−13z;z=−9

2.41

n7=−21;n=−147n7=−21;n=−147

2.42

n8=−56;n=−448n8=−56;n=−448

2.43

q−8=72;q=−576q−8=72;q=−576

2.44

p−9=81;p=−729p−9=81;p=−729

2.45

25f=16;f=4025f=16;f=40

2.46

34f=21;f=2834f=21;f=28

2.47

58+x=14;x=3858+x=14;x=38

2.48

34+x=56;x=11234+x=56;x=112

2.49

$0.39

2.50

$5.83

2.51

$120,000

2.52

21 flats

2.53

x=−4x=−4

2.54

a=−8a=−8

2.55

y=5y=5

2.56

m=9m=9

2.57

n=−10n=−10

2.58

c=−1c=−1

2.59

p=−7p=−7

2.60

m=−3m=−3

2.61

j=2j=2

2.62

h=1h=1

2.63

x=−1x=−1

2.64

y=4y=4

2.65

q=1q=1

2.66

n=1n=1

2.67

a=−5a=−5

2.68

k=−6k=−6

2.69

x=10x=10

2.70

y=−3y=−3

2.71

x=−5x=−5

2.72

y=−5y=−5

2.73

x=4x=4

2.74

y=1y=1

2.75

y=−6y=−6

2.76

z=8z=8

2.77

m=2m=2

2.78

n=2n=2

2.79

u=2u=2

2.80

x=4x=4

2.81

j=53j=53

2.82

k=52k=52

2.83

p=−2p=−2

2.84

q=−8q=−8

2.85

y=175y=175

2.86

z=0z=0

2.87

n=1n=1

2.88

m=−1m=−1

2.89

identity; all real numbers

2.90

identity; all real numbers

2.91

conditional equation; q=911q=911

2.92

conditional equation; k=20114k=20114

2.93

contradiction; no solution

2.94

contradiction; no solution

2.95

x=12x=12

2.96

x=−2x=−2

2.97

x=12x=12

2.98

u=−12u=−12

2.99

x=−1x=−1

2.100

c=−2c=−2

2.101

p=−4p=−4

2.102

q=2q=2

2.103

n=2n=2

2.104

m=−1m=−1

2.105

y=2y=2

2.106

z=−2z=−2

2.107

b=−20b=−20

2.108

c=−6c=−6

2.109

r=1r=1

2.110

s=−8s=−8

2.111

h=12h=12

2.112

k=−1k=−1

2.113

n=9n=9

2.114

d=16d=16

2.115

330 miles

2.116

7 miles

2.117

11 hours

2.118

56 mph

2.119

r=45r=45 r=dtr=dt

2.120

r=65r=65 r=dtr=dt

2.121

h=20h=20 h=2Abh=2Ab

2.122

b=4b=4 b=2Ahb=2Ah

2.123

$12,000 P=IrtP=Irt

2.124

$9,000 P=IrtP=Irt

2.125

y=1y=1 y=103x4y=103x4

2.126

y=−1y=−1 y=185x2y=185x2

2.127

b=Pacb=Pac

2.128

c=Pabc=Pab

2.129

y=94x7y=94x7

2.130

y=15x8y=15x8

2.131

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the left of the bracket.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the left of the parenthesis.
2.132

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 2 is graphed on the number line, with an open parenthesis at x equals negative 2, and a dark line extending to the right of the parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 3 is graphed on the number line, with an open parenthesis at x equals negative 3, and a dark line extending to the left of the parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the right of the bracket.
2.133

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 2 comma infinity, parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 1.5, bracket.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 3/4 is graphed on the number line, with an open bracket at x equals 3/4, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 3/4 comma infinity, parenthesis.
2.134

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 4 is graphed on the number line, with an open bracket at x equals negative 4, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 4, bracket.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 0.5 is graphed on the number line, with an open bracket at x equals 0.5, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, o.5 comma infinity, parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 2/3 is graphed on the number line, with an open parenthesis at x equals negative 2/3, and a dark line extending to the left of the parenthesis. The inequality is also written in interval notation as parenthesis, negative infinity comma negative 2/3, parenthesis.
2.137

c>8c>8

This figure is a number line ranging from 6 to 10 with tick marks for each integer. The inequality c is greater than 8 is graphed on the number line, with an open parenthesis at c equals 8, and a dark line extending to the right of the parenthesis.
2.138

(-∞,5](-∞,5]

This figure is a number line ranging from 3 to 7 with tick marks for each integer. The inequality d is less than or equal to 5 is graphed on the number line, with an open bracket at d equals 5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 5, bracket.
2.139

q>−4q>−4

This figure is a number line ranging from negative 6 to negative 3 with tick marks for each integer. The inequality q is greater than negative 4 is graphed on the number line, with an open parenthesis at q equals negative 4, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 4 comma infinity, parenthesis.

Section 2.1 Exercises

1.

yes

3.

no

5.

x=11x=11

7.

y=−111y=−111

9.

b=12b=12

11.

p=−11.7p=−11.7

13.

a=121a=121

15.

m=−182m=−182

17.

x=73x=73

19.

y=13.8y=13.8

21.

x=−255x=−255

23.

z=−9.02z=−9.02

25.

q=14q=14

27.

p=1615p=1615

29.

c=25c=25

31.

x=1x=1

33.

x=0x=0

35.

y=24y=24

37.

u=−7.1u=−7.1

39.

a=−30a=−30

41.

y=28y=28

43.

n=−50n=−50

45.

j=8j=8

47.

a=114a=114

49.

x=13x=13

51.

x+9=52;x=43x+9=52;x=43

53.

m10=−14;m=−4m10=−14;m=−4

55.

y+(−30)=40;y=70y+(−30)=40;y=70

57.

9x8x=107;1079x8x=107;107

59.

n16=12;23n16=12;23

61.

−4n+5n=−82;82−4n+5n=−82;82

63.

11 miles

65.

7 years old

67.

21 pounds

69.

100.5 degrees

71.

$121.19

73.

d=1724inchd=1724inch

75.

No. Justifications will vary.

Section 2.2 Exercises

77.

x=7x=7

79.

c=−11c=−11

81.

y=80915y=80915

83.

p=54137p=54137

85.

z=13z=13

87.

x=0x=0

89.

x=140x=140

91.

q=100q=100

93.

y=−144y=−144

95.

m=−540m=−540

97.

y=−6y=−6

99.

v=72v=72

101.

y=72y=72

103.

w=−64w=−64

105.

a=−4a=−4

107.

x=203x=203

109.

p=79p=79

111.

u=14u=14

113.

p=−12p=−12

115.

n=88n=88

117.

d=15d=15

119.

q=−11q=−11

121.

x=725x=725

123.

x=100x=100

125.

y=9y=9

127.

w=−198w=−198

129.

a=92a=92

131.

x=−2x=−2

133.

m=27m=27

135.

p=2130p=2130

137.

y=−7y=−7

139.

c=51c=51

141.

x=8x=8

143.

133=−19n;n=−7133=−19n;n=−7

145.

−152=8q;q=−19−152=8q;q=−19

147.

r12=−48;r=−576r12=−48;r=−576

149.

j−20=−80;j=1,600j−20=−80;j=1,600

151.

b−6=18;b=−108b−6=18;b=−108

153.

k22=−66;k=−1,452k22=−66;k=−1,452

155.

310x=15;x=50310x=15;x=50

157.

52v=50;v=2052v=50;v=20

159.

25+f=12;f=11025+f=12;f=110

161.

q18=34;q=78q18=34;q=78

163.

6 balloons

165.

$1.08

167.

36 mpg

169.

$195,000

171.

15 49-cent stamps

173.

Answers will vary.

Section 2.3 Exercises

175.

x=6x=6

177.

y=6y=6

179.

m=−8m=−8

181.

b=−8b=−8

183.

x=−4x=−4

185.

q=97q=97

187.

k=−11k=−11

189.

x=9x=9

191.

b=−3b=−3

193.

z=3z=3

195.

x=34x=34

197.

r=−2r=−2

199.

x=19x=19

201.

f=7f=7

203.

q=−5q=−5

205.

c=−4c=−4

207.

x=2x=2

209.

p=85p=85

211.

y=4y=4

213.

m=−6m=−6

215.

a=7a=7

217.

a=−40a=−40

219.

p=15p=15

221.

z=3.46z=3.46

223.

w=60w=60

225.

x=23x=23

227.

30 feet

229.

x=2x=2 Justifications will vary.

231.

Yes. Justifications will vary.

Section 2.4 Exercises

233.

y=3y=3

235.

n=−2n=−2

237.

p=43p=43

239.

t=−9t=−9

241.

b=2b=2

243.

m=6m=6

245.

k=32k=32

247.

t=1t=1

249.

x=−2x=−2

251.

x=5x=5

253.

d=1d=1

255.

r=−7r=−7

257.

m=−15m=−15

259.

y=−4y=−4

261.

w=12w=12

263.

a=4a=4

265.

r=8r=8

267.

m=3m=3

269.

y=−3y=−3

271.

x=34x=34

273.

x=−6x=−6

275.

n=−1n=−1

277.

a=−4a=−4

279.

m=−4m=−4

281.

d=−3d=−3

283.

k=35k=35

285.

n=−5n=−5

287.

v=1v=1

289.

p=−34p=−34

291.

m=−4m=−4

293.

identity; all real numbers

295.

identity; all real numbers

297.

conditional equation; d=23d=23

299.

conditional equation; n=7n=7

301.

contradiction; no solution

303.

contradiction; no solution

305.

conditional equation; k=26k=26

307.

contradiction; no solution

309.

identity; all real numbers

311.

identity; all real numbers

313.

8 nickels

315.

Answers will vary.

317.

Answers will vary.

Section 2.5 Exercises

319.

x=1x=1

321.

y=−1y=−1

323.

b=−2b=−2

325.

x=3x=3

327.

n=−24n=−24

329.

x=−4x=−4

331.

z=−2z=−2

333.

a=1a=1

335.

x=−6x=−6

337.

x=1x=1

339.

q=7q=7

341.

x=52x=52

343.

m=−1m=−1

345.

p=−4p=−4

347.

v=20v=20

349.

d=−24d=−24

351.

y=−1y=−1

353.

v=4v=4

355.

y=15y=15

357.

k=2k=2

359.

x=20x=20

361.

x=22x=22

363.

x=8x=8

365.

n=19n=19

367.

d=10d=10

369.

q=15q=15

371.

s=35s=35

373.

Answers will vary.

375.

100. Justifications will vary.

Section 2.6 Exercises

377.

290 miles

379.

30 miles

381.

5 hours

383.

11.25 hours

385.

75 mph

387.

75 mph

389.

t=4t=4 t=drt=dr

391.

t=3.5t=3.5 t=drt=dr

393.

r=70r=70 r=dtr=dt

395.

r=40r=40 r=dtr=dt

397.

h=16h=16 h=2Abh=2Ab

399.

b=10b=10 b=2Ahb=2Ah

401.

P=$13,166.67P=$13,166.67 P=IrtP=Irt

403.

t=2t=2 years t=IPrt=IPr

405.

y=−5y=−5 y=105x2y=105x2

407.

y=17y=17 y=54xy=54x

409.

a=90ba=90b

411.

c=180abc=180ab

413.

y=139xy=139x

415.

y=−1+5xy=−1+5x

417.

y=113x3y=113x3

419.

y=3+xy=3+x

421.

W=P2L2W=P2L2

423.

π=Cdπ=Cd

425.

H=VLWH=VLW

427.

10°C

429.

Answers will vary.

Section 2.7 Exercises

431.

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 1 is graphed on the number line, with an open parenthesis at x equals 1, and a dark line extending to the right of the parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 2 is graphed on the number line, with an open parenthesis at x equals negative 2, and a dark line extending to the left of the parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 3 is graphed on the number line, with an open bracket at x equals negative 3, and a dark line extending to the right of the bracket.
433.

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to 0 is graphed on the number line, with an open bracket at x equals 0, and a dark line extending to the left of the bracket.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than negative 4 is graphed on the number line, with an open parenthesis at x equals negative 4, and a dark line extending to the right of the parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1 is graphed on the number line, with an open bracket at x equals negative 1, and a dark line extending to the right of the bracket.
435.

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 3 is graphed on the number line, with an open parenthesis at x equals 3, and a dark line extending to the right of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, 3 comma infinity, parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 0.5 is graphed on the number line, with an open bracket at x equals negative 0.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 0.5, bracket.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1/3 is graphed on the number line, with an open bracket at x equals 1/3 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 1/3 comma infinity, parenthesis.
437.

  1. This figure is a number line with tick marks. The inequality x is less than or equal to 5 is graphed on the number line, with an open bracket at x equals 5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 5, bracket.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 1.5 comma infinity, parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 7/3 is graphed on the number line, with an open parenthesis at x equals negative 7/3 (written in), and a dark line extending to the left of the parenthsis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 7/3, parenthesis.
439.
At the top of this figure is the solution to the inequality: m is less than or equal to 107. Below this is a number line ranging from 105 to 109 with tick marks for each integer. The inequality x is less than or equal to 107 is graphed on the number line, with an open bracket at x equals 107, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 107, bracket.
441.
At the top of this figure is the solution to the inequality: v is greater than negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality x is greater than negative 9 is graphed on the number line, with an open parenthesis at x equals negative 9, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 9 comma infinity, parenthesis.
443.
At the top of this figure is the solution to the inequality: b is greater than or equal to negative 17/24. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to negative 17/24 is graphed on the number line, with an open bracket at b equals negative 17/24 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 17/24 comma infinity, parenthesis.
445.
At the top of this figure is the solution to the inequality: g is less than 23/26. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality g is less than 23/26 is graphed on the number line, with an open parenthesis at g equals 23/26 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 23/26, parenthesis.
447.
At the top of this figure is the solution to the inequality: y is less than 8. Below this is a number line ranging from 6 to 10 with tick marks for each integer. The inequality y is less than 8 is graphed on the number line, with an open parenthesis at y equals 8, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 8, parenthesis.
449.
At the top of this figure is the solution to the inequality: s is greater than or equal to 9. Below this is a number line ranging from 7 to 11 with tick marks for each integer. The inequality s is greater than or equal to 9 is graphed on the number line, with an open bracket at s equals 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 9 comma infinity, parenthesis.
451.
At the top of this figure is the solution to the inequality: v is greater than or equal to negative 12. Below this is a number line ranging from negative 14 to negative 10 with tick marks for each integer. The inequality v is greater than or equal to negative 12 is graphed on the number line, with an open bracket at v equals negative 12, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 12 comma infinity, parenthesis.
453.
At the top of this figure is the solution to the inequality: d is less than negative 15. Below this is a number line ranging from negative 17 to negative 13 with tick marks for each integer. The inequality d is less than negative 15 is graphed on the number line, with an open parenthesis at d equals negative 15, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 15, parenthesis.
455.
At the top of this figure is the solution to the inequality: k is greater than 64. Below this is a number line ranging from 62 to 66 with tick marks for each integer. The inequality k is greater than 64 is graphed on the number line, with an open parenthesis at k equals 64, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 64, parenthesis.
457.
At the top of this figure is the solution to the inequality: g is less than or equal to 16. Below this is a number line ranging from 14 to 18 with tick marks for each integer. The inequality g is less than or equal to 16 is graphed on the number line, with an open bracket at g equals 16, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 16, bracket.
459.
At the top of this figure is the solution to the inequality: b is less than or equal to negative 300. Below this is a number line ranging from negative 302 to negative 298 with tick marks for each integer. The inequality b is less than or equal to negative 300 is graphed on the number line, with an open bracket at b equals negative 300, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 300, bracket.
461.
At the top of this figure is the solution to the inequality: q is greater than 108. Below this is a number line ranging from 106 to 110 with tick marks for each integer. The inequality q is greater than 108 is graphed on the number line, with an open parenthesis at q equals 108, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 108 comma infinity, parenthesis.
463.
At the top of this figure is the solution to the inequality: s is less than negative 4. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality s is less than negative 4 is graphed on the number line, with an open parenthesis at s equals negative 4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 4, parenthesis.
465.
At the top of this figure is the solution to the inequality: x is less than or equal to negative 75. Below this is a number line ranging from negative 77 to negative 73 with tick marks for each integer. The inequality x is less than or equal to negative 75 is graphed on the number line, with an open bracket at x equals negative 75, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 75, bracket.
467.
At the top of this figure is the solution to the inequality: au is greater than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality u is greater than or equal to 7 is graphed on the number line, with an open bracket at u equals 7, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 7 comma infinity, parenthesis.
469.
At the top of this figure is the solution to the inequality: p is less than 18/5. Below this is a number line ranging from 2 to 6 with tick marks for each integer. The inequality p is less than 18/5 is graphed on the number line, with an open parenthesis at p equals 18/5 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 18/5, parenthesis.
471.
At the top of this figure is the solution to the inequality: y is less than negative 5. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality y is less than negative 5 is graphed on the number line, with an open parenthesis at y equals negative 5, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 5, parenthesis.
473.
At the top of this figure is the solution to the inequality: x is less than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality x is less than or equal to 7 is graphed on the number line, with an open bracket at x equals 7, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 7, bracket.
475.
At the top of this figure is the solution to the inequality: the inequality is an identity. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma infinity, parenthesis.
477.
At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: “No solution”.
479.
At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: “No solution”.
481.
At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: “No solution”.
483.
At the top of this figure is the solution to the inequality: k is greater than or equal to negative 11/5. Below this is a number line ranging from negative 4 to 0 with tick marks for each integer. The inequality k is greater than or equal to negative 11/5 is graphed on the number line, with an open bracket at k equals negative 11/5 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 11/5 comma infinity, parenthesis.
485.
At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: “No solution”.
487.
At the top of this figure is the solution to the inequality: y is greater than or equal to 10/49. Below this is a number line ranging from negative 1 to 3 with tick marks for each integer. The inequality y is greater than or equal to 10/49 is graphed on the number line, with an open bracket at y equals 10/49 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 10/49 comma infinity, parenthesis.
489.
At the top of this figure is the solution to the inequality: d is greater than negative 90. Below this is a number line ranging from negative 92 to negative 88 with tick marks for each integer. The inequality d is greater than negative 90 is graphed on the number line, with an open parenthesis at d equals negative 90, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 90 comma infinity, parenthesis.
491.
At the top of this figure is the solution to the inequality: n is less than or equal to negative 78. Below this is a number line ranging from negative 80 to negative 76 with tick marks for each integer. The inequality n is less than or equal to negative 78 is graphed on the number line, with an open bracket at n equals negative 78, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 78, bracket.
493.
At the top of this figure is the the inequality 90c is less than 450. Below this is the solution to the inequality: c is less than 5. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma 5, parenthesis. Below the interval notation is a number line ranging from 3 to 7 with tick marks for each integer. The inequality c is less than 5 is graphed on the number line, with an open parenthesis at c equals 5, and a dark line extending to the left of the parenthesis.
495.
At the top of this figure is the the inequality 10y is less than or equal to negative 110. Below this is the solution to the inequality: y is less than or equal to negative 11. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma negative 11, bracket. Below the interval notation is a number line ranging from negative 13 to negative 9 with tick marks for each integer. The inequality y is less than or equal to negative 11 is graphed on the number line, with an open bracket at y equals negative 11, and a dark line extending to the left of the bracket.
497.
At the top of this figure is the the inequality k plus 6 is greater than 25. Below this is the solution to the inequality: k is greater than 19. Below the the solution written in interval notation: parenthesis, 19 comma infinity, parenthesis. Below the interval notation is a number line ranging from 17 to 21 with tick marks for each integer. The inequality k is greater than 19 is graphed on the number line, with an open parenthesis at k equals 19, and a dark line extending to the right of the parenthesis.
499.
At the top of this figure is the the inequality x minus 12 is greater than or equal to 21. Below this is the solution to the inequality: x is greater than or equal to 33. Below the solution is the solution written in interval notation: bracket, 33 comma infinity, parenthesis. Below the interval notation is a number line ranging from 32 to 36 with tick marks for each integer. The inequality x is greater than or equal to 33 is graphed on the number line, with an open bracket at x equals 33, and a dark line extending to the right of the bracket.
501.
At the top of this figure is the the inequality negative 2s is less than 56. Below this is the solution to the inequality: s is greater than negative 28. Below the solution is the solution written in interval notation: parenthesis, negative 28 comma infinity, parenthesis. Below the interval notation is a number line ranging from negative 30 to negative 26 with tick marks for each integer. The inequality s is greater than negative 28 is graphed on the number line, with an open parenthesis at s equals negative 28, and a dark line extending to the right of the parenthesis.
503.
At the top of this figure is the the inequality a minus 15 is greater than or equal to negative 7. Below this is the solution to the inequality: a is greater than or equal to 8. Below the solution is the solution written in interval notation: bracket, 8 comma infinity, parenthesis. Below the interval notation is a number line ranging from 0 to 10 with tick marks for each integer. The inequality a is greater than or equal to 8 is graphed on the number line, with an open bracket at a equals 8, and a dark line extending to the right of the bracket.
505.

h77h77

507.

n8n8

509.

Answers will vary.

511.

Answers will vary.

Review Exercises

513.

no

515.

yes

517.

y=−8y=−8

519.

n=1.5n=1.5

521.

x=5x=5

523.

p=18.8p=18.8

525.

y=−25y=−25

527.

d=12.1d=12.1

529.

x=−8x=−8

531.

p=−28p=−28

533.

n4=13;n=17n4=13;n=17

535.

161 pounds

537.

$131.19

539.

a=−5a=−5

541.

y=−4y=−4

543.

y=−300y=−300

545.

u=32u=32

547.

c=324c=324

549.

y=118y=118

551.

x=−1x=−1

553.

d=3d=3

555.

b9=−27;b=−243b9=−27;b=−243

557.

s112=14;s=13s112=14;s=13

559.

$32

561.

w=7w=7

563.

n=−4n=−4

565.

a=−7a=−7

567.

x=38x=38

569.

n=−5n=−5

571.

c=32c=32

573.

p=132p=132

575.

n=12n=12

577.

m=−14m=−14

579.

q=18q=18

581.

x=−1x=−1

583.

k=34k=34

585.

contradiction; no solution

587.

identity; all real numbers

589.

x=15x=15

591.

k=41k=41

593.

y=−1y=−1

595.

u=−85u=−85

597.

y=47y=47

599.

5 hours

601.

37.5 miles

603.

r=82mphr=82mph; r=Dtr=Dt

605.

h=17h=17 h=2Abh=2Ab

607.

y=143y=143 y=64x3y=64x3

609.

H=VLWH=VLW

611.

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 0 is graphed on the number line, with an open parenthesis at x equals 0, and a dark line extending to the right of the parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than negative 3 is graphed on the number line, with an open parenthesis at x equals negative 3, and a dark line extending to the left of the parenthesis.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 1 is graphed on the number line, with an open bracket at x equals 1, and a dark line extending to the right of the bracket.
613.

  1. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than 2 is graphed on the number line, with an open parenthesis at x equals 2, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 2 comma infinity, parenthesis.

  2. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is less than or equal to negative 1.5 is graphed on the number line, with an open bracket at x equals negative 1.5, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 1.5, bracket.

  3. This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. The inequality x is greater than or equal to 5/3 is graphed on the number line, with an open bracket at x equals 5/3, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 5/3 comma infinity, parenthesis.
615.
At the top of this figure is the solution to the inequality: m is less than or equal to 42. Below this is a number line ranging from 40 to 44 with tick marks for each integer. The inequality m is less than or equal to 42 is graphed on the number line, with an open bracket at m equals 42, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 42, bracket
617.
At the top of this figure is the solution to the inequality: b is greater than or equal to 3/8. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to 3/8 is graphed on the number line, with an open bracket at b equals 3/8 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 3/8 comma infinity, bracket
619.
At the top of this figure is the solution to the inequality: d is greater than or equal to negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality d is greater than or equal to negative 9 is graphed on the number line, with an open bracket at d equals negative 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 9 comma infinity, parenthesis.
621.
At the top of this figure is the solution to the inequality: q is less than or equal to 48. Below this is a number line ranging from 46 to 50 with tick marks for each integer. The inequality q is less than or equal to 48 is graphed on the number line, with an open bracket at q equals 48, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 48, bracket.
623.
At the top of this figure is the solution to the inequality: h is greater than or equal to 15. Below this is a number line ranging from 13 to 17 with tick marks for each integer. The inequality h is greater than or equal to 15 is graphed on the number line, with an open bracket at h equals 15, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 15 comma infinity, parenthesis.
625.
At the top of this figure is the solution to the inequality: a is less than negative 6. Below this is a number line ranging from negative 8 to negative 4 with tick marks for each integer. The inequality a is less than negative 6 is graphed on the number line, with an open parenthesis at a equals negative 6, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 6, parenthesis.
627.
At the top of this figure is the inequality c minus 3 is greater than or equal to 360. To the right of this is the solution to the inequality: c is greater than or equal to 363. To the right of the solution is the solution written in interval notation: bracket, 363 comma infinity, parenthesis. Below all of this is a number line ranging from 361 to 365 with tick marks for each integer. The inequality c is greater than or equal to 363 is graphed on the number line, with an open bracket at c equals 363, and a dark line extending to the right of the bracket.
629.
At the top of this figure is the inequality negative 2a is less than or equal to 8. To the right of this is the solution to the inequality: a is greater than or equal to negative 4. To the right of the solution is the solution written in interval notation: bracket, negative 4 comma infinity, parenthesis. Below all of this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality a is greater than or equal to negative 4 is graphed on the number line, with an open bracket at a equals negative 4, and a dark line extending to the right of the bracket.

Practice Test

631.

no yes

633.

c=32c=32

635.

x=−5x=−5

637.

x=9x=9

639.

y=−4y=−4

641.

m=9m=9

643.

d=−14d=−14

645.

x=13x=13

647.

p=103p=103

649.

contradiction; no solution

651.

y=4y=4 y=5x2y=5x2

653.
This figure is a number line ranging from 1 to 5 with tick marks for each integer. The inequality x is less than 11/4 is graphed on the number line, with an open parenthesis at x equals 11/4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 11/4, parenthesis.
655.
This figure is a number line ranging from negative 2 to 3 with tick marks for each integer. The inequality c is greater than 1/3 is graphed on the number line, with an open parenthesis at c equals 1/3, and a dark line extending to the right of the parenthesis. Below the number line is the solution: c is greater than 1/3. To the right of the solution is the solution written in interval notation: parenthesis, 1/3 comma infinity, parenthesis
657.

n+1548;n33n+1548;n33

659.

120=23p120=23p; The original price was $180.

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