Beginning and Intermediate Algebra: An Integrated Approach (6th Edition)

1121 Pages·2010·172.27 MB·English

by  R. David Gustafson

Beginning
and Intermediate
Algebra
Books in the Gustafson/Karr/Massey Series
Beginning Algebra, Ninth Edition
Beginning and Intermediate Algebra: An Integrated
Approach, Sixth Edition
Intermediate Algebra, Ninth Edition
Beginning
and Intermediate
Algebra
6th Edition
An Integrated Approach
R. David Gustafson
Rock Valley College
Rosemary M. Karr
Collin College
Marilyn B. Massey
Collin College
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Beginning and Intermediate Algebra: An © 2011, 2008Brooks/Cole, Cengage Learning
Integrated Approach,Sixth Edition
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About the Authors
R. DAVID GUSTAFSON
R.DavidGustafsonisProfessorEmeritusof MathematicsatRockValleyCollegeinIlli-
noisandalsohas taughtextensivelyatRockfordCollegeandBeloitCollege.Heiscoauthor
of severalbest-sellingmathematicstextbooks,includingGustafson/Frisk/Hughes,College
Algebra;Gustafson/Karr/Massey,BeginningAlgebra,IntermediateAlgebra,Beginningand
Intermediate Algebra: A Combined Approach; and the Tussy/Gustafson and Tussy/
Gustafson/Koenig developmental mathematics series. His numerous professional honors
include Rock Valley Teacher of the Year and Rockford’s Outstanding Educator of the
Year.HehasbeenveryactiveinAMATYCasaMidwestVice-presidentandhasbeenPres-
identofIMACC,AMATYC’sIllinoisaffiliate.HeearnedaMasterofArts degree in Math-
ematics from Rockford College in Illinois, as well as a Master of Science degree from
NorthernIllinoisUniversity.
ROSEMARY M. KARR
Rosemary Karr graduated from Eastern Kentucky University (EKU) with a Bachelor’s
degree in Mathematics, attained her Master of Arts degree at EKU in Mathematics Edu-
cation, and earned her Ph.D. from the University of North Texas. After two years of
teaching high school mathematics, she joined the faculty at Eastern Kentucky University,
where she earned tenure as Assistant Professor of Mathematics. A professor of mathe-
matics at Collin College in Plano, Texas, since 1990, Professor Karr has written more
than 10 solutions manuals, presented numerous papers, and been an active member in
several educational associations (including President of the National Association for
Developmental Education). She has been honored several times by Collin College, and
has received such national recognitions as U.S. Professor of the Year (2007).
MARILYN B. MASSEY
Marilyn Massey teaches mathematics at Collin College in McKinney, Texas, where she
joined the faculty in 1991. She has been President of the Texas Association for Develop-
mental Education, featured on the list of Who’s Who Among America’s Teachers and
received an Excellence in Teaching Award from the National Conference for College
Teaching and Learning. Professor Massey has presented at numerous state and national
conferences; her article “Service-Learning Projects in Data Interpretation”was one of
two included from community college instructors for the Mathematical Association of
America’s publication, Mathematics in Service to the Community.She earned her Bache-
lor’s degree from the University of North Texas and Master of Arts degree in Mathemat-
ics Education from the University of Texas at Dallas.
v
To Craig, Jeremy, Paula, Gary, Bob,
Jennifer, John-Paul, Gary, and Charlie
RDG
To my husband and best friend Fred,
for his unwavering support of my work
RMK
To my parents, Dale and Martha,
for their lifelong encouragement, and
to Ron, for his unconditional love and support
MBM
Contents
1
Chapter Real Numbers and Their Basic Properties 1
1.1 Real Numbers and Their Graphs 2
1.2 Fractions 13
1.3 Exponents and Order of Operations 30
1.4 Adding and Subtracting Real Numbers 41
1.5 Multiplying and Dividing Real Numbers 50
1.6 Algebraic Expressions 58
1.7 Properties of Real Numbers 66
(cid:2) PROJECTS 74
CHAPTER REVIEW 75
CHAPTER 1 TEST 82
2
Chapter Equations and Inequalities 83
2.1 Solving Basic Linear Equations in One Variable 84
2.2 Solving More Linear Equations in One Variable 98
2.3 Simplifying Expressions to Solve Linear Equations in One Variable 107
2.4 Formulas 115
2.5 Introduction to Problem Solving 122
2.6 Motion and Mixture Problems 131
2.7 Solving Linear Inequalities in One Variable 139
(cid:2) PROJECTS 148
CHAPTER REVIEW 148
CHAPTER 2 TEST 154
CUMULATIVE REVIEW EXERCISES 155
vii
viii Contents
3
Chapter Graphing and Solving Systems of Linear
Equations and Linear Inequalities 157
3.1 The Rectangular Coordinate System 158
3.2 Graphing Linear Equations 169
3.3 Solving Systems of Linear Equations by Graphing 184
3.4 Solving Systems of Linear Equations by Substitution 196
3.5 Solving Systems of Linear Equations by Elimination (Addition) 202
3.6 Solving Applications of Systems of Linear Equations 210
3.7 Solving Systems of Linear Inequalities 221
(cid:2) PROJECTS 235
CHAPTER REVIEW 236
CHAPTER 3 TEST 243
4
Chapter Polynomials 245
4.1 Natural-Number Exponents 246
4.2 Zero and Negative-Integer Exponents 254
4.3 Scientific Notation 261
4.4 Polynomials and Polynomial Functions 268
4.5 Adding and Subtracting Polynomials 279
4.6 Multiplying Polynomials 287
4.7 Dividing Polynomials by Monomials 297
4.8 Dividing Polynomials by Polynomials 303
(cid:2) PROJECTS 311
CHAPTER REVIEW 311
CHAPTER 4 TEST 316
CUMULATIVE REVIEW EXERCISES 317
5
Chapter Factoring Polynomials 319
5.1 Factoring Out the Greatest Common Factor; Factoring by Grouping 320
5.2 Factoring the Difference of Two Squares 329
5.3 Factoring Trinomials with a Leading Coefficient of 1 335
5.4 Factoring General Trinomials 345
5.5 Factoring the Sum and Difference of Two Cubes 354
5.6 Summary of Factoring Techniques 359
5.7 Solving Equations by Factoring 363
5.8 Problem Solving 369
(cid:2) PROJECTS 376
CHAPTER REVIEW 377
CHAPTER 5 TEST 381
Contents ix
6
Chapter Rational Expressions and Equations; Ratio
and Proportion 382
6.1 Simplifying Rational Expressions 383
6.2 Multiplying and Dividing Rational Expressions 392
6.3 Adding and Subtracting Rational Expressions 402
6.4 Simplifying Complex Fractions 414
6.5 Solving Equations That Contain Rational Expressions 421
6.6 Solving Applications of Equations That Contain Rational Expressions 428
6.7 Ratios 434
6.8 Proportions and Similar Triangles 440
(cid:2) PROJECTS 452
CHAPTER REVIEW 452
CHAPTER 6 TEST 459
CUMULATIVE REVIEW EXERCISES 460
7
Chapter More Equations, Inequalities, and Factoring 461
7.1 Review of Solving Linear Equations and Inequalities in One Variable 462
7.2 Solving Equations in One Variable Containing Absolute Values 475
7.3 Solving Inequalities in One Variable Containing an Absolute-Value Term 481
7.4 Review of Factoring 488
7.5 Review of Rational Expressions 501
7.6 Synthetic Division 514
(cid:2) PROJECTS 521
CHAPTER REVIEW 523
CHAPTER 7 TEST 531
8
Chapter Writing Equations of Lines, Functions,
and Variation 532
8.1 A Review of the Rectangular Coordinate System 533
8.2 Slope of a Line 542
8.3 Writing Equations of Lines 554
8.4 A Review of Functions 567
8.5 Graphs of Nonlinear Functions 577
8.6 Variation 591
(cid:2) PROJECTS 600
CHAPTER REVIEW 601
CHAPTER 8 TEST 608
CUMULATIVE REVIEW EXERCISES 609