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IGNACIO BELLO

INTRODUCTORY

algebraA REA L-W ORLD APPROA CHTHIRD EDITION

Ignacio Bello

Hillsborough Community College Tampa, Florida

INTRODUCTORY ALGEBRA: A REAL-WORLD APPROACH, THIRD EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Previous edition 2006. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network 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. 1 2 3 4 5 6 7 8 9 0 QPV/QPV 0 9 8 ISBN 9780073533438 MHID 0073533432

ISBN 9780073199696 (Annotated Instructors Edition) MHID 0073199699

Editorial Director: Stewart K. Mattson Senior Sponsoring Editor: David Millage Developmental Editor: Michelle Driscoll Marketing Manager: Victoria Anderson Senior Project Manager: Vicki Krug Senior Production Supervisor: Sherry L. Kane Senior Media Project Manager: Sandra M. Schnee Senior Designer: David W. Hash Cover/Interior Designer: Asylum Studios (USE) Cover Image: Royalty-Free/CORBIS Senior Photo Research Coordinator: Lori Hancock Photo Research: Connie Mueller Supplement Coordinator: Melissa M. Leick Compositor: ICC Macmillan Inc. Typeface: 10/12 Times Roman Printer: Quebecor World Versailles, KY

The credits section for this book begins on page C-1 and is considered an extension of the copyright page.

www.mhhe.com

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About the Author

Ignacio Belloattended the University of South Florida (USF), where he earned a B.A. and M.A. in Mathematics. He began teaching at USF in 1967, and in 1971 he became a member of the Faculty at Hillsborough Community College (HCC) and Coordinator of the Math and Sciences Department. Professor Bello instituted the USF/HCC remedial program, a program that started with 17 students taking Intermediate Algebra and grew to more than 800 students with courses covering Developmental English, Reading, and Mathematics. Aside from the present series of books (Basic College Mathematics, Introductory Algebra, and Intermediate Algebra), Professor Bello is the author of more than 40 textbooks including Topics in Contemporary Mathematics, College Algebra, Algebra and Trigonometry, and Business Mathematics. Many of these textbooks have been translated into Spanish. With Professor Fran Hopf, Bello started the Algebra Hotline, the only live, college-level television help program in Florida. Professor Bello is featured in three television programs on the award-winning Education Channel. He has helped create and develop the USF Mathematics Department Website (http://mathcenter.usf.edu), which serves as support for the Finite Math, College Algebra, Intermediate Algebra, and Introductory Algebra, and CLAST classes at USF. You can see Professor Bellos presentations and streaming videos at this website, as well as at http://www. ibello.com. Professor Bello is a member of the MAA and AMATYC and has given many presentations regarding the teaching of mathematics at the local, state, and national levels.

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ContentsPreface ix Guided Tour: Features and Supplements xvi Applications Index xxvi

Chapter

r

R

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Prealgebra ReviewR. 1 R. 2Fractions: Building and Reducing 2 Operations with Fractions and Mixed Numbers 9 R. 3 Decimals and Percents 20 Collaborative Learning 32 Practice Test R 33

Chapter

one

1

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Real Numbers and Their PropertiesThe Human Side of Algebra 35 1 . 1 Introduction to Algebra 36 1 . 2 The Real Numbers 42 1 . 3 Adding and Subtracting Real Numbers 51 1 . 4 Multiplying and Dividing Real Numbers 59 1 . 5 Order of Operations 68 1 . 6 Properties of the Real Numbers 76 1 . 7 Simplifying Expressions 86 Collaborative Learning 97 Research Questions 98 Summary 98 Review Exercises 100 Practice Test 1 102

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Contents

Chapter

two

2

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Equations, Problem Solving, and InequalitiesThe Human Side of Algebra 105 2 . 1 The Addition and Subtraction Properties of Equality 106 2 . 2 The Multiplication and Division Properties of Equality 118 2 . 3 Linear Equations 131 2 . 4 Problem Solving: Integer, General, and Geometry Problems 143 2 . 5 Problem Solving: Motion, Mixture, and Investment Problems 153 2 . 6 Formulas and Geometry Applications 165 2 . 7 Properties of Inequalities 179 Collaborative Learning 193 Research Questions 193 Summary 194 Review Exercises 196 Practice Test 2 199 Cumulative Review Chapters 12 201

Chapter

three

3

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Graphs of Linear Equations, Inequalities, and ApplicationsThe Human Side of Algebra 203 3 . 1 Line Graphs, Bar Graphs, and Applications 204 3 . 2 Graphing Linear Equations in Two Variables 220 3 . 3 Graphing Lines Using Intercepts: Horizontal and Vertical Lines 234 3 . 4 The Slope of a Line: Parallel and Perpendicular Lines 249 3 . 5 Graphing Lines Using Points and Slopes 259 3 . 6 Applications of Equations of Lines 267 3 . 7 Graphing Inequalities in Two Variables 274 Collaborative Learning 285 Research Questions 286 Summary 287 Review Exercises 289 Practice Test 3 294 Cumulative Review Chapters 13 303v

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Contents

Chapter

four

4

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Exponents and PolynomialsThe Human Side of Algebra 307 4 . 1 The Product, Quotient, and Power Rules for Exponents 308 4 . 2 Integer Exponents 319 4 . 3 Application of Exponents: Scientic Notation 329 4 . 4 Polynomials: An Introduction 337 4 . 5 Addition and Subtraction of Polynomials 348 4 . 6 Multiplication of Polynomials 358 4 . 7 Special Products of Polynomials 366 4 . 8 Division of Polynomials 378 Collaborative Learning 385 Research Questions 385 Summary 385 Review Exercises 387 Practice Test 4 390 Cumulative Review Chapters 14 392

Chapter

ve

5

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FactoringThe Human Side of Algebra 395 5 . 1 Common Factors and Grouping 396 5 . 2 Factoring x2 bx c 407 5 . 3 Factoring ax2 bx c, a 1 414 5 . 4 Factoring Squares of Binomials 425 5 . 5 A General Factoring Strategy 432 5 . 6 Solving Quadratic Equations by Factoring 440 5 . 7 Applications of Quadratics 449 Collaborative Learning 458 Research Questions 459 Summary 460 Review Exercises 461 Practice Test 5 464 Cumulative Review Chapters 15 466

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Contents

six

6

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Rational ExpressionsThe Human Side of Algebra 469 6 . 1 Building and Reducing Rational Expressions 470 6 . 2 Multiplication and Division of Rational Expressions 486 6 . 3 Addition and Subtraction of Rational Expressions 496 6 . 4 Complex Fractions 507 6 . 5 Solving Equations Containing Rational Expressions 512 6 . 6 Ratio, Proportion, and Applications 522 6 . 7 Direct and Inverse Variation 533 Collaborative Learning 541 Research Questions 541 Summary 542 Review Exercises 543 Practice Test 6 547 Cumulative Review Chapters 16 549

Chapter

seven

7

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Solving Systems of Linear Equations and InequalitiesThe Human Side of Algebra 551 7 . 1 Solving Systems of Equations by Graphing 552 7 . 2 Solving Systems of Equations by Substitution 569 7 . 3 Solving Systems of Equations by Elimination 578 7 . 4 Coin, General, Motion, and Investment Problems 588 7 . 5 Systems of Linear Inequalities 597 Collaborative Learning 603 Research Questions 604 Summary 605 Review Exercises 606 Practice Test 7 608 Cumulative Review Chapters 17 610

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Contents

Chapter

eight

8

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Roots and RadicalsThe Human Side of Algebra 613 8 . 1 Finding Roots 614 8 . 2 Multiplication and Division of Radicals 621 8 . 3 Addition and Subtraction of Radicals 628 8 . 4 Simplifying Radicals 634 8 . 5 Applications: Solving Radical Equations 642 Collaborative Learning 649 Research Questions 650 Summary 650 Review Exercises 651 Practice Test 8 653 Cumulative Review Chapters 18 655

Chapter

nine

9

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Quadratic EquationsThe Human Side of Algebra 659 9 . 1 Solving Quadratic Equations by the Square Root Property 660 9 . 2 Solving Quadratic Equations by Completing the Square 670 9 . 3 Solving Quadratic Equations by the Quadratic Formula 680 9 . 4 Graphing Quadratic Equations 689 9 . 5 The Pythagorean Theorem and Other Applications 700 9 . 6 Functions 707 Collaborative Learning 716 Research Questions 717 Summary 717 Review Exercises 718 Practice Test 9 721 Cumulative Review Chapters 19 725

Selected Answers SA-1 Photo Credits C-1 Index I-1viii

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Preface

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From the AuthorThe Inspiration for My TeachingI was born in Havana, Cuba, and I encountered some of the same challenges in mathematics that many of my current students face, all while attempting to overcome a language barrier. In high school, I failed my freshman math course, which at the time was a complex language for me. However, perseverance being one of my traits, I scored 100% on the nal exam the second time around. After working in various jobs (roofer, sheetrock installer, and dock worker), I nished high school and received a college academic scholarship. I enrolled in calculus and made a C. Never one to be discouraged, I became a math major and learned to excel in the courses that had previously frustrated me. While a graduate student at the University of South Florida (USF), I taught at a technical school, Tampa Technical Institute, a decision that contributed to my resolve to teach math and make it