Intermediate Algebra

1027 Pages·2011·21.706 MB·English

by  Alan S. Tussy, R. David Gustafson, Diane R. Koenig

Get the most out of each worked example
by using all of its features.
EXAMPLE 1 Here, we state the given problem.
Strategy Then, we explain what will be done to solve the problem.
WHY Next, we explain why it will be done this way.
T he steps that follow show how the problem is solved by using
Solution
the given strategy.
1ST STEP
The given problem = The result of 1ST STEP This author note explains
the 1ST Step
2ND STEP
=
The result of 2ND STEP This author note explains
the 2ND Step
3RD STEP
= The result of 3RD STEP This author note explains
(the answer) the 3RD Step
Self Check 1 A Similar Problem
After reading the example, Now Try Problem 45
try the Self Check problem
to test your understanding.
The answer is given at the
end of the section, right
After you work the Self Check,
before the Study Set.
you are ready to try a similar
problem in the Guided Practice
section of the Study Set.
EDITION
4
INTERMEDIATE
ALGEBRA
ALAN S.TUSSY
CITRUS COLLEGE
R.DAVID GUSTAFSON
ROCK VALLEY COLLEGE
DIANE R.KOENIG
ROCK VALLEY COLLEGE
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Intermediate Algebra,Fourth Edition © 2011, 2006Brooks/Cole, Cengage Learning
Alan S. Tussy, R. David Gustafson, Diane R. Koenig
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1 2 3 4 5 6 7 14 13 12 11 10
To the mathematics instructors of Edgewood High School,the University
of Redlands,and California State University at Los Angeles,
whose love of their discipline and dedication to their students
continue to be an inspiration to me
ALAN S.TUSSY
To my wife,Carol,whose support has been invaluable
R.DAVID GUSTAFSON
To my husband,Brian,with love;and my daughters,
Ashley,Brianna,and Carly,whom I love very much and who bring me great joy
DIANE R.KOENIG
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C O N T E N T S
Study Skills Workshop S-1
CHAPTER 1
A Review of Basic Algebra 1
1.1
The Language of Algebra 2
1.2
The Real Numbers 10
1.3
Operations with Real Numbers 23
1.4 Simplifying Algebraic Expressions Using Properties mages
of Real Numbers 37 Getty I
1.5 Solving Linear Equations Using Properties of Equality 49 midt/
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1.8
More about Problem Solving 83
THINK IT THROUGH Fastest Growing Occupations 86
Chapter Summary and Review 98
Chapter Test 112
CHAPTER 2
Graphs,Equations of Lines,and Functions 115
2.1
The Rectangular Coordinate System 116
2.2
Graphing Linear Equations 128
2.3
Rate of Change and the Slope of a Line 143
THINK IT THROUGH Community Colleges 148
2.4 Writing Equations of Lines 156 m/iofoto
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2.6
Graphs of Functions 186
Chapter Summary and Review 201
Chapter Test 211
Cumulative Review 213
v
vi Contents
CHAPTER 3
Systems of Equations 215
3.1
Solving Systems of Equations by Graphing 216
THINK IT THROUGH Bachelor’s Degrees 220
3.2
Solving Systems of Equations Algebraically 228
3.3
Problem Solving Using Systems of Two Equations 237
my 3.4 Solving Systems of Equations in Three Variables 254
Ala
mages/ 3.5 Problem Solving Using Systems of Three Equations 262
© Radius I 3.6 Solving Systems of Equations Using Matrices 270
3.7
Solving Systems of Equations Using Determinants 280
Chapter Summary and Review 291
Chapter Test 301
Cumulative Review 303
CHAPTER 4
Inequalities 305
4.1
Solving Linear Inequalities in One Variable 306
THINK IT THROUGH Changing Values 307
4.2
Solving Compound Inequalities 319
THINK IT THROUGH Study Abroad 326
w Brookes/Corbis 44..34 SLionlevianrg In Aebqsuoalulittiee sV ainlu Tew Eoq Vuaartiiaobnlse sand I3n4e2qualities 331
Andre 4.5 Systems of Linear Inequalities 351
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Chapter Summary and Review 361
Chapter Test 369
Cumulative Review 371
Contents vii
CHAPTER 5
Exponents,Polynomials,and Polynomial
Functions 375
5.1
Exponents 376
5.2
Scientific Notation 388
THINK IT THROUGH The American Educational System 390
5.3
Polynomials and Polynomial Functions 396
5.4 Multiplying Polynomials 410 Alamy
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of Two Cubes 429 ©
5.7
Factoring Trinomials 437
5.8
Summary of Factoring Techniques 448
5.9
Solving Equations by Factoring 451
Chapter Summary and Review 462
Chapter Test 473
Cumulative Review 475
CHAPTER 6
Rational Expressions and Equations 477
6.1
Rational Functions and Simplifying Rational Expressions 478
THINK IT THROUGH Learning and Remembering 481
6.2
Multiplying and Dividing Rational Expressions 491
6.3 Adding and Subtracting Rational Expressions 501 mages
6.4 Simplifying Complex Fractions 512 Getty I
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Solving Rational Equations 540
6.8
Problem Solving Using Rational Equations 551
6.9
Proportion and Variation 560
Chapter Summary and Review 576
Chapter Test 589
Cumulative Review 591
viii Contents
CHAPTER 7
Radical Expressions,Equations,
and Functions 595
7.1
Radical Expressions and Radical Functions 596
7.2
Simplifying and Combining Radical Expressions 611
7.3
Multiplying and Dividing Radical Expressions 621
7.4
m/Sean Locke 7.5 SRoatlvioinnga lR Eaxdpicoanle Enqtusatio6n4s2 632
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7.7
Complex Numbers 665
Chapter Summary and Review 679
Chapter Test 689
Cumulative Review 691
CHAPTER 8
Quadratic Equations,Functions,
and Inequalities 693
8.1
The Square Root Property and Completing the Square 694
8.2
The Quadratic Formula 706
8.3
Quadratic Functions and Their Graphs 717
Getty Images T8H.I4NK IT THROUGH Automobile Accidents 726
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© I Chapter Summary and Review 756
Chapter Test 764
Cumulative Review 766