INTRODUCTORY ALGEBRA D. FRANKLIN WRIGHT CERRITOS COLLEGE Title Page.indd 310/3/2007 3:53:03 PM © All Rights Reser ved.Editor: Nina Miller Project Editor: Larry Wadsworth Jr. Developmental Editor: Marcel Prevuznak Production Editors: Phillip Bushkar, Kimberly Cumbie Answer Key Editors: Larien Acosta, Eric Wilder Editorial Assistants: Bethany Bates, Mandy Glover, D. Kanthi, B. Syam Prasad Layout: QSI (Pvt.) Ltd.: U. Nagesh, E. Jeevan Kumar Art: Ayvin Samonte Cover Art and Design: Johnson Design A division of Quant Systems, Inc. Copyright © 2009 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher. Library of Congress Control Number: 2007934775 Printed in the United States of America ISBN: Student: 978-1-932628-32-6 Student Bundle: 978-1-932628-33-3 Title Page.indd 410/3/2007 3:53:03 PM © All Rights Reser ved.iii CONTENTS Hawkes Learning Systems: Introductory Algebra xx R.1 Exponents and Order of Operations 2 R.2 Prime Numbers, Factoring, and LCM 14 R.3 Fractions (Multiplication and Division) 24 R.4 Fractions (Addition and Subtraction) 37 R.5 Decimals and Percents 47 Chapter R Index of Key Ideas and Terms 64 Chapter R Chapter Review 69 Chapter R Chapter Test 72 CHAPTER R Review of Basic Topics 1 1.1 The Real Number Line and Absolute Value 76 1.2 Addition with Integers 90 1.3 Subtraction with Integers 96 1.4 Multiplication and Division with Real Numbers 106 1.5 Properties of Real Numbers 118 Chapter 1 Index of Key Ideas and Terms 125 Chapter 1 Chapter Review 129 Chapter 1 Chapter Test 133 CHAPTER 1 Integers and Real Numbers 75 2.1 Simplifying and Evaluating Algebraic Expressions 136 2.2 Multiplication and Division with Fractions 143 2.3 Addition and Subtraction with Fractions 153 2.4 Decimal Numbers and Fractions 162 2.5 Order of Operations with Negative Numbers and Fractions 171 2.6 Translating English Phrases and Algebraic Expressions 179 Chapter 2 Index of Key Ideas and Terms 186 Chapter 2 Chapter Review 190 Chapter 2 Chapter Test 194 Chapter 2 Cumulative Review 196 CHAPTER 2 Fractions with Variables and Algebraic Expressions 135 Preface vii Table of Contents3.indd 310/3/2007 4:09:56 PM © All Rights Reser ved.Contents iv 3.1 Solving Linear Equations: x + b = c and ax = c 200 3.2 Solving Linear Equations: ax + b = c 213 3.3 More Linear Equations: ax + b = dx + c 220 3.4 Solving Linear Inequalities and Applications 228 3.5 Working with Formulas 240 3.6 Applications: Number Problems and Consecutive Integers 251 3.7 Applications: Percent Problems (Discount, Taxes, Commission, Profit, and Others) 261 3.8 Formulas in Geometry 271 Chapter 3 Index of Key Ideas and Terms 282 Chapter 3 Chapter Review 288 Chapter 3 Chapter Test 293 Chapter 3 Cumulative Review 296 CHAPTER 3 Solving Equations and Inequalities 199 4.1 The Cartesian Coordinate System and Reading Graphs 302 4.2 Graphing Linear Equations in Two Variables: Ax + By = C 320 4.3 The Slope-Intercept Form: y = mx + b 333 4.4 The Point-Slope Form: y - y 1 = m( x - x 1 ) 350 4.5 Introduction to Functions and Function Notation 361 4.6 Graphing Linear Inequalities: y < mx + b 373 Chapter 4 Index of Key Ideas and Terms 383 Chapter 4 Chapter Review 387 Chapter 4 Chapter Test 393 Chapter 4 Cumulative Review 396 CHAPTER 4 Graphing Linear Equations and Inequalities in Two Variables 301 5.1 Systems of Equations: Solutions by Graphing 402 5.2 Systems of Equations: Solutions by Substitution 414 5.3 Systems of Equations: Solutions by Addition 420 5.4 Applications: Distance-Rate-Time, Number Problems, Amounts and Costs 429 5.5 Applications: Interest and Mixture 440 5.6 Graphing Systems of Linear Inequalities 449 Chapter 5 Index of Key Ideas and Terms 454 Chapter 5 Chapter Review 457 Chapter 5 Chapter Test 460 Chapter 5 Cumulative Review 462 CHAPTER 5 Systems of Linear Equations 401 Table of Contents3.indd 410/3/2007 4:09:56 PM © All Rights Reser ved.v Contents 6.1 Exponents 468 6.2 Exponents and Scientific Notation 481 6.3 Introduction to Polynomials 495 6.4 Addition and Subtraction with Polynomials 502 6.5 Multiplication with Polynomials 508 6.6 Special Products of Binomials 515 6.7 Division with Polynomials 525 Chapter 6 Index of Key Ideas and Terms 534 Chapter 6 Chapter Review 537 Chapter 6 Chapter Test 541 Chapter 6 Cumulative Review 543 CHAPTER 6 Exponents and Polynomials 467 7.1 Greatest Common Factor and Factoring by Grouping 548 7.2 Factoring Trinomials: x2 + bx + c 559 7.3 More on Factoring Trinomials: ax2 + bx + c 566 7.4 Factoring Special Products: Difference of Two Squares and Perfect Square Trinomials 579 7.5 Solving Quadratic Equations by Factoring 586 7.6 Applications of Quadratic Equations 594 7.7 Additional Applications of Quadratic Equations 602 Chapter 7 Index of Key Ideas and Terms 606 Chapter 7 Chapter Review 611 Chapter 7 Chapter Test 615 Chapter 7 Cumulative Review 617 CHAPTER 7 Factoring Polynomials and Solving Quadratic Equations 547 8.1 Reducing Rational Expressions 622 8.2 Multiplication and Division with Rational Expressions 633 8.3 Addition and Subtraction with Rational Expressions 639 8.4 Complex Algebraic Fractions 647 8.5 Solving Proportions and Other Equations with Rational Expressions 654 8.6 Applications 665 8.7 Additional Applications: Variation 675 Chapter 8 Index of Key Ideas and Terms 682 Chapter 8 Chapter Review 686 Chapter 8 Chapter Test 691 Chapter 8 Cumulative Review 693 CHAPTER 8 Rational Expressions 621 Table of Contents3.indd 510/3/2007 4:09:57 PM © All Rights Reser ved.Contents vi 9.1 Real Numbers and Evaluating Radicals 698 9.2 Simplifying Radicals 711 9.3 Addition, Subtraction, and Multiplication with Radicals 720 9.4 Rationalizing Denominators 726 9.5 Solving Equations with Radicals 732 9.6 Rational Exponents 738 9.7 The Pythagorean Theorem 744 Chapter 9 Index of Key Ideas and Terms 758 Chapter 9 Chapter Review 762 Chapter 9 Chapter Test 766 Chapter 9 Cumulative Review 768 CHAPTER 9 Real Numbers and Radicals 697 10.1 Quadratic Equations: The Square Root Method 772 10.2 Quadratic Equations: Completing the Square 781 10.3 Quadratic Equations: The Quadratic Formula 788 10.4 Applications 796 10.5 Quadratic Functions: y = ax2 + bx + c 808 Chapter 10 Index of Key Ideas and Terms 821 Chapter 10 Chapter Review 823 Chapter 10 Chapter Test 827 Chapter 10 Cumulative Review 829 CHAPTER 10 Quadratic Equations 771 A.1 Difference of Two Cubes and Sum of Two Cubes 833 A.2 Pi 838 APPENDIX 833 ANSWERS 841 INDEX 884 Table of Contents3.indd 610/3/2007 4:09:57 PM © All Rights Reser ved.vii Preface PREFACE Purpose and Style Introductory Algebra (sixth edition) provides a smooth transition from arithmetic (or prealgebra) to the more abstract skills and reasoning abilities developed in a beginning algebra course. With feedback from users, insightful comments from reviewers, and skillful editing and design by the editorial staff at Hawkes Publishing, I have confidence that students and instructors alike will find that this text is indeed a superior teaching and learning tool. In particular, new in this edition, Chapter R (Review of Basic Topics) is designed to help students review basic arithmetic knowledge in exponents, order of operations, prime numbers, factoring, least common multiple (LCM), fractions, decimals, and percents. This chapter can be treated as part of the course or simply review for the students at their convenience. The text may be used independently or in conjunction with the software package Hawkes Learning Systems: Introductory Algebra developed by Quant Systems/Hawkes Learning Systems. The writing style gives carefully worded, thorough explanations that are direct, easy to understand and mathematically accurate. The use of color, boldface, subheading, and shaded boxes helps students understand and reference important topics. Each topic is developed in a straightforward step-by-step manner. Each section contains many detailed examples to lead students successfully through the exercises and help them develop an understanding of the related algebraic concepts. Practice problems with answers are provided in almost every section to allow students to “warm up” and to provide instructors with immediate classroom feedback. Reading graphs and topics from geometry are integrated within the discussions and problems. For example circle graphs and bar graphs are used in discussions as early as Chapter R and in Chapter 1. Students are encouraged to use calculators when appropriate and explicit directions and diagrams are provided as they relate to a TI-84 Plus calculator. The emphasis is on the use of calculators as aids with the understanding that calculators do not take the place of critical thinking and analysis. Preface.indd 710/3/2007 4:14:10 PM © All Rights Reser ved.Preface viii The NCTM and AMATYC curriculum standards have been taken into consideration in the development of the topics throughout the text. In particular: • there is emphasis on reading and writing skills as they relate to mathematics, • techniques for using a graphing calculator are discussed early and detailed instructions are included to help in graphing linear inequalities (Section 4.6), in finding the solutions to systems of two linear equations (Section 5.1), and in graphing systems of two linear inequalities (Section 5.6), • a special effort has been made to make the exercises motivating and interesting, and • special exercises titled “Writing and Thinking About Mathematics” are designed to help students develop writing skills related to mathematical thinking. Preface.indd 810/3/2007 4:14:10 PM © All Rights Reser ved.ix Preface ix Did You Know?: A feature at the beginning of every chapter presents some interesting math history related to the chapter at hand. Objectives: The objectives provide the students with a clear and concise list of skills presented in each section. Introduction: Presented before the fi rst section of every chapter, this feature provides an introduction to the subject of the chapter and its purpose. Features Preface.indd 910/3/2007 4:14:13 PM © All Rights Reser ved.Next >