Elementary Algebra For College Students /

Contents

Preface

To the Student

1 Real Numbers

1.1 Study Skills for Success in Mathematics 2

1.2 Problem Solving 7

1.3 Fractions 20

1.4 The Real Number System 30

1.5 Inequalities 35

Mid-Chapter Test: Sections 1.1-1.5 40

1.6 Addition of Real Numbers 41

1.7 Subtraction of Real Numbers 50

1.8 Multiplication and Division of Real Numbers 60

1.9 Exponents, Parentheses, and the Order of Operations 68

1.10 Properties of the Real Number System 80

Chapter 1 Summary 86

Chapter 1 Review Exercises 91

Chapter 1 Practice Test 94

Solving Linear Equations and Inequalities

2.1 Combining Like Terms 96

2.2 The Addition Property of Equality

105

2.3 The Multiplication Property of Equality 112

2.4 Solving Linear Equations with a Variable on Only

One Side of the Equation 119

Mid-Chapter Test: Sections 2.1-2.4

129

2.5 Solving Linear Equations with the Variable on Both Sides of the Equation 129

2.6 Formulas 140

2.7 Ratios and Proportions 152

2.8 Inequalities in One Variable

164

Chapter 2 Summary 171

Chapter 2 Review Exercises

175

Chapter 2 Practice Test

178

Cumulative Review Test 178

plications of Algebra

3.1 Changing Application Problems into Equations

180

3.2 Solving Application Problems 195

Mid-Chapter Test: Sections 3.1-3.2

206

3.3 Geometric Problems

207
SULTAR

O TRABAJOS

ADÉMICOS

CENTRO DEFORMACIÓN

Contants

402

7 Factoring

7.1 Factoring a Monomial from a Polynomial 403

7.2 Factoring by Grouping 410

7.3 Factoring Trinomials of the Form ax bxca-1 415

7.4 Factoring Trinomials of the Form ar

bx c01 424

Mid-Chapter Test: Sections 7.1-7.4 436

7.5 Special Factoring Formulas and a General Review of Factoring 436

7.6 Solving Quadratic Equations Using Factoring 444

7.7 Applications of Quadratic Equations 451

Chapter 7 Summary 458

Chapter 7 Review Exercises 461

Chapter 7 Practice Test 463

Cumulative Review Test 464

8 Rational Expressions and Equations

465

5

8.1 Simplifying Rational Expressions 466

8.2 Multiplication and Division of Rational Expressions 474

8.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least

Common Denominator 482

8.4 Addition and Subtraction of Rational Expressions

489

Mid-Chapter Test: Sections 8.1-8.4 496

8.5 Complex Fractions 497

8.6 Solving Rational Equations 502

8.7 Rational Equations: Applications and Problem Solving

510

8.8 Variation 522

Chapter 8 Summary 529

Chapter 8 Review Exercises

532

Chapter 8 Practice Test 534

Cumulative Review Test 535

Roots and Radicals

9.1 Evaluating Square Roots

537

9.2 Simplifying Square Roots 544

9.3 Adding, Subtracting, and Multiplying Square Roots

550

9.4 Dividing Square Roots 556

Mid-Chapter Test: Sections 9.1-9.4 564

9.5 Solving Radical Equations 565

9.6 Radicals: Applications and Problem Solving

9.7 Higher Roots and Rational Exponents

571

Chapter 9 Summary 585

578

Chapter 9 Review Exercises

588

Chapter 9 Practice Test 590

Cumulative Review Test 591
Contents

F

10 Quadratic Equations

10.1 The Square Root Property 593

10.2 Solving Quadratic Equations by Completing the Square 598

10.3 Solving Quadratic Equations by the Quadratic Formula 604

Mid-Chapter Test: Sections 10.1-10.3

614

10.4 Graphing Quadratic Equations 615

10.5 Complex Numbers 625

Chapter 10 Summary 628

Chapter 10 Review Exercises 630

Chapter 10 Practice Test 632

Cumulative Review Test 633

Appendices

Appendix A Review of Decimals and Percent

634

Appendix B Finding the Greatest Common Factor and Least Common Denominator 637

Appendix C Geometry 640

Answers

Graphing Answers

Applications Index

Subject Index

Photo Credits

Preface

T written for college students and other hits who have have never been reposed to atgshes of those who have been exposed but need a rebesher coarse My primary goal was to write a book that students can read, understand and enjoy. To achieve this gool I have used short sentencos, cleat explanations, and many de tnded, work.cd-out examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text

Features of the Text

Full-Color Format Color is used pedagogically in the following ways

Important definitions and procedures are color screened

Color screening color type is used to make other important items stand out.

Artwork is enhanced and clarified with use of multiple colors

The full-color format allows for easy identification of important features by students.

The full-color format makes the text more appealing and interesting to students.

Readability One of the most important features of the text is its readability. The book is very readable, even for those with weak reading skills Short, clear sentences are used and more easily recognized, and casy-to-understand language is used whenever possible.

Accuracy Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typo-graphical errors and have checked all the answers.

Connections Many of our students do not thoroughly rasp new concepts the first time they are presented. In ais text we encourage students to make connections. That we introduce a concept, then later in the text briefly introduce it and build upon it. Often an important con-pt is used in many sections of the text. Students are re-nded where the material was seen before, or where it be used again. Thus also serves to emphasize the im-tance of the concept. Important concepts are also rein-red throughout the text in the Cumulative Review. reises and Cumulative Review Tests.

pter Opening Application Each chapter begins a real-life application related to the material covered

in the chapter Be theίστε τα δωρίσ thes should have theke the

Goals of this Chapter the feature on the chagnar

opener page gives students preview of the chapter other chapters of the book. This material helpedes see the connections among varines topics in the book and the connection to real world situations

The Use of icons At the begining of each eserene t the icon for MathXL Mathix and for MyMathLab stant are illustrated. Both of these icons will be cxplained shortly

Keyed Section Objectives Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portaoms of the sections with blue numbers such as

Problem Solving Polya's five-step problem-solving procedure discussed in Section 1.2. Throughout the book, problem solving and Polya's problem-solving proce dure are emphasized.

Practical Applications Practical applications of alge bra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applica tions motivates students.

Detailed, Worked-Out Examples A wealth of ex amples have been worked out in a step-by-step, detailed manner. Important steps are highlighted in color, and no steps are omitted until after the student has seen a suffi cient number of similar examples

Now Try Exercises In each section, after each exam-ple, students are asked to work an exercise that parallels the example given in the text. These Now Try Exercises make the students active, rather than passive, learners and they reinforce the concepts as students work the exercises Through these exercises, students have the opportunity to immediately apply what they have learned. After each ex-

ample, Now Try Exercises are indicated in green type such as Now Try Exercise 27 They are a

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