Essentials of College algebra /

Contents

Prefour vi

Supplements Guide xi

R Review of Basic Concepts/

R.1 Real Numbers and Their Properties 2

Sexs of Numbers and the Number Line

Exponens

Order of Op

Properties of Real Numbers

R.2 Order and Absolute Value 16

Order on the Number Line

Absolute Value

Properties of A

R.3 Polynomials 24

Rules for Exponents Polnomials Addition and Saberпастел

Multiplication

Divin

R.4 Factoring Polynomials 37

Factoring Out the Greatest Common Factor Factoring by Grimping

Factoring Trinomials

Factorany Himonials

Factoring by Sabaton

R.5 Rational Expressions 46

Rational Expressions

Lowest Term of a Rational Expresstom

Complex Fractions

Multiplication and

Division Achdition and Sobtraction

R.6 Rational Exponents 55

Negative Exponents and the Quotient Rule

Rational Exponen Complex

Fractions Revisited

Simplified Radicals Radical Notation

Operations with Radicals

R.7 Radical Expressions 65

Rationalizing Denominators

Summary 76

Review Exercises 79

Test 83

Quantitative Reasoning 84

1 Equations and Inequalities

85

1.1 Linear Equations 86

Basic Terminology of Equations Solving Linear Equation

Identities

Conditional Equations, and Contradictions Solving for a Specifient Variable

(Lateral Equations)

Applications and Modeling with Linear Equations 92

1.2

Solving Applied Problems

Geometry Problems

Motion Problems Modeling with Linear Equations

Work Rate Problems

Mixture Problems

1.3 Complex Numbers 107

Basic Concepts of Complex Numbers

Operations on Complex Numbers

1.4 Quadratie Equations 115

Solving a Quadratic Equation Completing the Square

Formula

The Discriminant Solving for a Specified Variable

The Quadru
4.6

Applications and Models of Exponential Growth and Decay

452

The Exponential Growth or Decay Fonction Decay Function Models Growth Function Models

Summary 464

Review Exercises 467

Test 471.

473

Quantitative Reasoning 472

5 Other Topics in Algebra

5.1 Systems of Linear Equations 474

Elimination Method

Substitution Method Linear Systems Systems Unknowns (Variables) Applying Systems of Equations Using Systems of Equations to Model Data

Special Solving Linear Systems with Three

Summary Exercises on Systems of Equations

491

5.2 Sequences and Series 492

Summation Properties

Sequences Series and Summation Notation

5.3 Arithmetic Sequences and Series 503

Arithmetic Sequences

Arithmetic Series

5.4 Geometric Sequences and Series

512

Geometric Sequences Geometric Series Annuities

Infinite Geometric Series

Summary Exercises on Sequences and Series 523

Summary 525

Review Exercises

528

Test 531

Quantitative Reasoning 5.32

Appendix

Sets

533

Glossary 539

Solutions to Selected Exercises S-1

Answers to Selected Exercises A-1

Index of Applications

1-1

Index 1-5

Preface

In Essentials of College Algebra, we continue our ongoing commitment to pro-viding the best possible text to help instructors teach and students succeed. To help students develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathe-matical topic in the text using a systematic approach designed to actively engage students in the learning process. We have tried to address the diverse needs of to-day's students through an open design, updated figures and graphs, helpful fea-tures, careful explanations of topics, and a comprehensive package of supple-ments and study aids. Students planning to continue their study of mathematics in calculus, trigonometry, statistics, or other disciplines, as well as those taking college algebra as their final mathematics course, will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the Annotated Instructor's Edition, which provides answers in the margins to almost all exercises, plus helpful Teaching Tips.

This text is a brief version of the Ninth Edition of our College Algebra text-book. It has been specifically designed to provide a more compact and less ex-pensive alternative to better meet the needs of colleges whose College Algebra courses do not include the more advanced topics covered in the longer text. To put it simply, we have focused the content of this book on helping students mas-ter the basic functions in college algebra and their graphs, while including a strong review of intermediate algebra at the beginning of the text and an intro duction to systems of linear equations and to sequences and series in Chapter 5. If you feel that the longer College Algebra textbook might be more suitable for your course, please contact your local Addison-Wesley representative to receive a copy.

Pedagogical Features

We are pleased to offer the following features

Chapter Openers These provide a quick preview of the chapter topics, plus a reference to a motivating application within the chapter.

Examples Step-by-step solutions to examples are easily identified using a Solution head. We have carefully polished all solutions and incorporated side comments and explanations, including helpful section references to previously covered material. Selected examples provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.

Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have incorporated many applied

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