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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

Try It

1.1

yes yes no yes
no

1.2

no yes yes no
no

1.3

2·2·2·2·52·2·2·2·5

1.4

2·2·3·52·2·3·5

1.5

3636

1.6

7272

1.7

16

1.8

23

1.9

86

1.10

1

1.11

9 64 40

1.12

216 64 185

1.13

10x2+16x+1710x2+16x+17

1.14

12y2+9y+712y2+9y+7

1.15

14x21314x213 12x÷212x÷2
z+13z+13 8x188x18

1.16

17y2+1917y2+19 7y7y
x+11x+11 11a1411a14

1.17

4(p+q)4(p+q) 4p+q4p+q

1.18

2x82x8 2(x8)2(x8)

1.19

w7w7

1.20

l6l6

1.21

4q84q8

1.22

7n+37n+3

1.23

== >> <<
==

1.24

>> == >>
<<

1.25

16

1.26

9

1.27

−6−6 2 −2−2

1.28

−7−7 3 −3−3

1.29

2 −2−2 −10−10 10

1.30

3 −3−3 −11−11 11

1.31

8,88,8 −18,−18, −18−18
19,1919,19 −4,−4, −4−4

1.32

8,88,8 −22,−22, −22−22
23,2323,23 3,33,3

1.33

3

1.34

13

1.35

23 60 −63−63 −9−9

1.36

39 39 −28 −7

1.37

81 −81−81

1.38

49 −49−49

1.39

4 21

1.40

9 6

1.41

31

1.42

67

1.43

(9+(−16))+4;3(9+(−16))+4;3

1.44

(−8+(−12))+7;13(−8+(−12))+7;13

1.45

The difference in temperatures was 45 degrees.

1.46

The difference in temperatures was 9 degrees.

1.47

23402340

1.48

5858

1.49

−33a−33a

1.50

−26b−26b

1.51

415415

1.52

2323

1.53

34b34b

1.54

4q4q

1.55

79607960

1.56

1036010360

1.57

27a323627a3236 2a32a3

1.58

24k53024k530 2k152k15

1.59

4

1.60

2

1.61

190190

1.62

272

1.63

2

1.64

2727

1.65

1212

1.66

2323

1.67

6.586.58 6.66.6 7

1.68

15.21815.218 15.2215.22
15.215.2

1.69

−16.49−16.49 −0.42−0.42

1.70

−23.593−23.593 −12.58−12.58

1.71

−27.4815−27.4815

1.72

−87.6148−87.6148

1.73

25.8 258 2,580

1.74

142 1,420 14,200

1.75

587.3587.3

1.76

34.2534.25

1.77

117500117500 −0.875−0.875

1.78

31253125 −0.375−0.375

1.79

0.09, 0.87, 0.039 17%, 175%, 8.25%

1.80

0.03, 0.91, 0.083 41%, 225%, 9.25%

1.81

6 13 −15−15

1.82

4 14 −10−10

1.83

4,494,49 −3,4,49−3,4,49
−3,0.3,95,4,49−3,0.3,95,4,49 22
−3,2,0.3,95,4,49−3,2,0.3,95,4,49

1.84

6,1216,121
25,−1,6,12125,−1,6,121
25,38,−1,6,12125,38,−1,6,121
2.041975...2.041975...
25,38,−1,6,121,2.041975...25,38,−1,6,121,2.041975...

1.87

Figure shows a number line with numbers ranging from 0 to 1. 0.6 is highlighted.

Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted, minus 0.25 is highlighted.
1.88

Figure shows a number line with numbers ranging from 0 to 1. 0.9 is highlighted.

Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted.
1.89

32r+29s32r+29s

1.90

41m+6n41m+6n

1.91

17151715

1.92

129129

1.93

−48a−48a

1.94

−92x−92x

1.95

549549

1.96

11251125

1.97

0 undefined

1.98

0 undefined

1.99

4x+84x+8

1.100

6x+426x+42

1.101

5y+35y+3

1.102

4n+94n+9

1.103

70+15p70+15p

1.104

4+35d4+35d

1.105

−10+15a−10+15a

1.106

−56+105y−56+105y

1.107

z+11z+11

1.108

x+4x+4

1.109

33x33x

1.110

2x202x20

1.111

5x665x66

1.112

7x137x13

Section 1.1 Exercises

1.

Divisible by 2, 3, 6

3.

Divisible by 2

5.

Divisible by 3, 5

7.

2·432·43

9.

5·7·135·7·13

11.

2·2·2·2·3·3·32·2·2·2·3·3·3

13.

24

15.

280

17.

440

19.

5

21.

58

23.

29

25.

149

27.

50

29.

5

31.

64 16 7

33.

21

35.

9

37.

10x+610x+6

39.

22a+122a+1

41.

17x2+20x+1617x2+20x+16

43.

5x26xy5x26xy 6y25x6y25x
y2+21y2+21 81x26x81x26x

45.

4ab2+3a2b4ab2+3a2b 20xy220xy2
m+15m+15 121x29x121x29x

47.

8(y9)8(y9) 8y98y9

49.

5(3x+y)5(3x+y) 15x+y15x+y

51.

2c+142c+14

53.

3n73n7

55.

Answers will vary.

57.

Answers will vary.

Section 1.2 Exercises

59.

>> >> >> >>

61.

== == >> ==

63.

0

65.

8

67.

15

69.

1

71.

−11−11 −3−3 33

73.

32

75.

−22−22

77.

2929

79.

6 −6−6 −20−20 2020

81.

−59−59

83.

22

85.

16 16

87.

45 45

89.

0

91.

4

93.

6

95.

−32−32 −65−65 −4−4
1313

97.

−4−4 −12−12 −39−39
1414

99.

6464 −64−64

101.

−47−47

103.

9090

105.

99

107.

4141

109.

−9−9

111.

−29−29

113.

11

115.

−3−3

117.

55

119.

−47−47 1616

121.

121121

123.

−56−56

125.

66

127.

(3+(−15))+7;5(3+(−15))+7;5

129.

10(−18);2810(−18);28
−2511;36−2511;36

131.

−6a+b−6a+b

133.

96°96°

135.

21 yards

137.

$28$28

139.

Answers will vary.

141.

Answers will vary.

Section 1.3 Exercises

143.

127127

145.

10211021

147.

2x23y2x23y

149.

21a211b221a211b2

151.

1313

153.

21502150

155.

11301130

157.

9n9n

159.

334x334x

161.

4949

163.

10u9v10u9v

165.

116116

167.

109109

169.

2525

171.

2m3n2m3n

173.

29242924

175.

148148

177.

1710517105

179.

53405340

181.

112112

183.

4x+3124x+312

185.

5656 44

187.

25n1625n16 25n163025n1630

189.

−8x1518−8x1518 10k2710k27

191.

−5(a+1)3−5(a+1)3 aa

193.

9797

195.

−8−8

197.

116116

199.

5252

201.

5454

203.

49254925

205.

154154

207.

521521

209.

5454

211.

124124

213.

−2815y60−2815y60

215.

33643364

217.

7979

219.

−5−5

221.

23242324

223.

115115

225.

11

227.

133133

229.

1515 6565

231.

1919

233.

511511

235.

Answers will vary.

237.

Answers will vary.

Section 1.4 Exercises

239.

5.78 5.8 6

241.

0.30 0.3 0

243.

63.48 63.5 63

245.

−40.91−40.91

247.

−7.22−7.22

249.

−27.5−27.5

251.

102.212102.212

253.

51.3151.31

255.

−4.89−4.89

257.

−1200.47982−1200.47982

259.

337.8914337.8914

261.

1.3051.305

263.

92.492.4

265.

2.5

267.

55200

269.

$2.44$2.44

271.

−4.8−4.8

273.

2.082.08

275.

125125

277.

1920019200

279.

0.850.85

281.

−12.4−12.4

283.

0.710.71

285.

0.3930.393

287.

156%156%

289.

6.25%6.25%

291.

8

293.

12

295.

−10−10

297.

0,36,90,36,9 −8,0,36,9−8,0,36,9 −8,0,125,36,9−8,0,125,36,9 1.95286...,1.95286..., −8,0,1.95286...,125,36,9−8,0,1.95286...,125,36,9

299.

none 100,−7,−1100,−7,−1
100,−7,83,−1,0.77,314100,−7,83,−1,0.77,314
none
100,−7,83,−1,0.77,314100,−7,83,−1,0.77,314

301.
Figure shows a number line with numbers ranging from 0 to 6. Some values are highlighted. From left to right, these are: 3 by 10, 11 by 6, 7 by 2 and 4.
303.
Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted. From left to right, these are: minus 5 by 2, minus 1 and two thirds, minus 3 by 4, 3 by 4, 1 and two thirds, and 5 by 2.
305.
Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 0 and 1.
307.
Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 3 and 4.
309.

Answers will vary.

311.

Answers will vary.

Section 1.5 Exercises

313.

27m+(−21n)27m+(−21n)

315.

54g+12h54g+12h

317.

2.43p+8.26q2.43p+8.26q

319.

−63−63

321.

156156

323.

1717

325.

14.8814.88

327.

10p10p

329.

4444

331.

7878

333.

dd

335.

49114911

337.

0

339.

undefined

341.

undefined

343.

32y+7232y+72

345.

6c786c78

347.

34q+334q+3

349.

5y35y3

351.

3+8r3+8r

353.

36d+9036d+90

355.

rs18rrs18r

357.

yp+4pyp+4p

359.

−28p7−28p7

361.

−3x+18−3x+18

363.

−3x+7−3x+7

365.

−3y8−3y8

367.

−33c+26−33c+26

369.

a+19a+19

371.

4m104m10

373.

72x2572x25

375.

22n+922n+9

377.

6c+346c+34

379.

12y+6312y+63

381.

Answers will vary.

383.

Answers will vary.

Review Exercises

385.

Divisible by 2,3,5,6,102,3,5,6,10

387.

120

389.

4

391.

3

393.

6x2x+56x2x+5

395.

11(y2)11(y2) 11y211y2

397.

== == >> ==

399.

−9−9

401.

8 −8−8 −22−22 22

403.

40 40

405.

−3−3 −15−15 −56−56 17

407.

28

409.

−12−12

411.

9

413.

(−4+(−9))+23;10(−4+(−9))+23;10

415.

46°46°

417.

15x311y215x311y2

419.

8x15y8x15y

421.

31363136

423.

118118 5656

425.

1616

427.

75

429.

1515

431.

6.176.17

433.

96.97896.978

435.

488.1813

437.

56.356.3

439.

−2.3−2.3

441.

485485

443.

1.27¯1.27¯

445.

4.75%4.75%

447.

no real number

449.
Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.
451.

34x+y34x+y

453.

1111511115

455.

917917

457.

undefined

459.

8b+108b+10

461.

xp5pxp5p

463.

−6x6−6x6

465.

6y+166y+16

Practice Test

467.

7n+77n+7

469.

−811;19−811;19

(−8(−3))+5;0(−8(−3))+5;0

471.

28.1528.15 28.14628.146

473.
Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.
475.

1

477.

−8−8

479.

15171517

481.

5353

483.

33

485.

7676

487.

−65.4−65.4

489.

−160

491.

18131813

493.

0 undefined

495.

13y313y3

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