Algebra for College Students, 5th Edition

978 Pages·2008·42.79 MB·English

by  Mark Dugopolski

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f i f t h e d i t i o n
Algebra
for College Students
Mark Dugopolski
Southeastern Louisiana University
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ALGEBRAFOR COLLEGE STUDENTS, FIFTH EDITION
Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the
Americas, New York, NY10020. Copyright ©2009 by The McGraw-Hill Companies, Inc. All rights
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or other electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside
the United States.
This book is printed on acid-free paper.
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ISBN 978–0–07–353352–0
MHID 0–07–353352–1
ISBN 978–0–07–320625–7 (Annotated Instructor’s Edition)
MHID 0–07–320625–3
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Library of Congress Cataloging-in-Publication Data
Dugopolski, Mark.
Algebra for college students / Mark Dugopolski. — 5th ed.
p. cm.
Includes index.
ISBN 978–0–07–353352–0 — ISBN 0–07–353352–1 (hard copy : alk. paper) 1. Algebra—
Textbooks. I. Title.
QA152.3.D837 2009
512.9—dc22
2007035865
www.mhhe.com
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In loving memory of my parents,
Walter and Anne Dugopolski
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About the Author
M
ark Dugopolski was born and raised in Menominee, Michigan. He received
a degree in mathematics education from Michigan State University and then
taught high school mathematics in the Chicago area. While teaching high
school, he received a master’s degree in mathematics from Northern Illinois
University. He then entered a doctoral program in mathematics at the University
ofIllinois in Champaign, where he earned his doctorate in topology in 1977. Hewas
then appointed to the faculty at Southeastern Louisiana University, where he taught
for 25 years. He is now professor emeritus of mathematics at SLU. He is a member
of MAA and AMATYC. He has written many articles and numerous mathematics
textbooks. He has a wife and two daughters. When he is not working, he enjoys
gardening, hiking, bicycling, jogging, tennis, fishing, and motorcycling.
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Contents
Preface xiii
Guided Tour: Features and Supplements xix
Applications Index xxx
1
The Real Numbers 1

r 1.1 Sets 2
e 1.2 The Real Numbers 9
t 1.3 Operations on the Set of Real Numbers 19
p 1.4 Evaluating Expressions 30
a 1.5 Properties of the Real Numbers 40
h 1.6 Using the Properties 48
C Chapter 1 Wrap-Up 56
• Summary 56
• Enriching Your Mathematical Word Power 58
• Review Exercises 59
• Chapter 1 Test 62
• Critical Thinking 64
2
Linear Equations and Inequalities
in One Variable 65

r 2.1 Linear Equations in One Variable 66
e 2.2 Formulas and Functions 78
t 2.3 Applications 89
p 2.4 Inequalities 102
a 2.5 Compound Inequalities 114
h 2.6 Absolute Value Equations and Inequalities 125
C Chapter 2 Wrap-Up 135
• Summary 135
• Enriching Your Mathematical Word Power 137
• Review Exercises 137
• Chapter 2 Test 142
• Making Connections: A Review of Chapters 1–2 143
• Critical Thinking 144
vii
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viii Contents
3
Linear Equations and Inequalities
in Two Variables 145

r 3.1 Graphing Lines in the Coordinate Plane 146
e 3.2 Slope of a Line 158
t 3.3 Three Forms for the Equation of a Line 170
p 3.4 Linear Inequalities and Their Graphs 183
a 3.5 Functions and Relations 199
h Chapter 3 Wrap-Up 211
C • Summary 211
• Enriching Your Mathematical Word Power 214
• Review Exercises 215
• Chapter 3 Test 220
• Making Connections: A Review of Chapters 1–3 223
• Critical Thinking 224
4
Systems of Linear Equations 225

r 4.1 Solving Systems by Graphing and Substitution 226
e 4.2 The Addition Method 238
t 4.3 Systems of Linear Equations in Three Variables 247
p 4.4 Solving Linear Systems Using Matrices 255
a 4.5 Determinants and Cramer’s Rule 264
h 4.6 Linear Programming 275
C Chapter 4 Wrap-Up 282
• Summary 282
• Enriching Your Mathematical Word Power 284
• Review Exercises 285
• Chapter 4 Test 288
• Making Connections: A Review of Chapters 1–4 289
• Critical Thinking 290
5
Exponents and Polynomials 291

r 5.1 Integral Exponents and Scientific Notation 292
e 5.2 The Power Rules 305
t 5.3 Polynomials and Polynomial Functions 314
p 5.4 Multiplying Binomials 323
a 5.5 Factoring Polynomials 331
h 5.6 Factoring ax2 (cid:1) bx (cid:1) c 341
C 5.7 Factoring Strategy 350
5.8 Solving Equations by Factoring 358
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Contents ix
Chapter 5 Wrap-Up 368
• Summary 368
• Enriching Your Mathematical Word Power 370
• Review Exercises 371
• Chapter 5 Test 374
• Making Connections: A Review of Chapters 1–5 375
• Critical Thinking 376
6
Rational Expressions and Functions 377

r 6.1 Properties of Rational Expressions and Functions 378
e 6.2 Multiplication and Division 388
t 6.3 Addition and Subtraction 396
p 6.4 Complex Fractions 407
a 6.5 Division of Polynomials 415
h 6.6 Solving Equations Involving Rational Expressions 425
C 6.7 Applications 433
Chapter 6 Wrap-Up 442
• Summary 442
• Enriching Your Mathematical Word Power 444
• Review Exercises 445
• Chapter 6 Test 449
• Making Connections: A Review of Chapters 1–6 451
• Critical Thinking 452
7
Radicals and Rational Exponents 453

r 7.1 Radicals 454
e 7.2 Rational Exponents 464
t 7.3 Adding, Subtracting, and Multiplying Radicals 475
p 7.4 Quotients, Powers, and Rationalizing Denominators 482
a 7.5 Solving Equations with Radicals and Exponents 491
h 7.6 Complex Numbers 502
C Chapter 7 Wrap-Up 511
• Summary 511
• Enriching Your Mathematical Word Power 513
• Review Exercises 514
• Chapter 7 Test 518
• Making Connections: A Review of Chapters 1–7 519
• Critical Thinking 520