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ALGEBRA DEMYSTIFIED Other Titles in the McGraw-Hill Demystified Series Astronomy Demystified by Stan Gibilisco Calculus Demystified by Steven G. Krantz Physics Demystified by Stan Gibilisco ALGEBRA DEMYSTIFIED RHONDA HUETTENMUELLER McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright ©2003 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, 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 permission of the publisher. 0-07-141210-7 The material in this eBook also appears in the print version of this title: 0-07-138993-8 All trademarks are trademarks of their respective owners. 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McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your require- ments or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inac- curacy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the pos- sibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. DOI: 10.1036/0071412107 To all those who struggle with math This page intentionally left blank. For more information about this book, click here. CONTENTS Preface ix CHAPTER 1 Fractions 1 CHAPTER 2 Introduction to Variables 37 CHAPTER 3 Decimals 55 CHAPTER 4 Negative Numbers 65 CHAPTER 5 Exponents and Roots 79 CHAPTER 6 Factoring 113 CHAPTER 7 Linear Equations 163 CHAPTER 8 Linear Applications 197 CHAPTER 9 Linear Inequalities 285 CHAPTER 10 Quadratic Equations 319 CHAPTER 11 Quadratic Applications 353 Appendix 417 Final Review 423 Index 437 vii Copyright 2003 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. This page intentionally left blank. PREFACE This book is designed to take the mystery out of algebra. Each section con- tains exactly one new idea—unlike most math books, which cover several ideas at once. Clear, brief explanations are followed by detailed examples. EachsectionendswithafewPracticeproblems,mostsimilartotheexamples. Solutions to the Practice problems are also given in great detail. The goal is to help you understand the algebra concepts while building your skills and confidence. Each chapter ends with a Chapter Review, a multiple-choice test designed to measure your mastery of the material. The Chapter Review could also be used as a pretest. If you think you understand the material in a chapter, take the Chapter Review test. If you answer all of the questions correctly, then youcansafelyskipthatchapter.Whentakingany multiple-choicetest,work the problems before looking at the answers. Sometimes incorrect answers look reasonable and can throw you off. Once you have finished the book, taketheFinalReview,whichisa multiple-choicetestbasedonmaterialfrom each chapter. Spend as much time in each section as you need. Try not to rush, but do makeacommitmenttolearningonaschedule.Ifyoufindaconceptdifficult, youmightneedtoworktheproblemsandexamplesseveraltimes.Trynotto jump around from section to section as most sections extend topics from previous sections. Not many shortcuts are used in this book. Does that mean you shouldn’t usethem?No.Whatyoushoulddoistrytofindtheshortcutsyourself.Once youhavefoundamethodthatseemstobeashortcut,trytofigureoutwhyit works. If you understand how a shortcut works, you are less likely to use it incorrectly (a common problem with algebra students). Because many find fraction arithmetic difficult, the first chapter is devoted almost exclusively to fractions. Make sure you understand the steps in this chapterbecausetheyarethesamestepsusedinmuchoftherestofthebook. For example, the steps used to compute 7 þ 5 are exactly those used to 2x 6 36 16 compute þ . x2þx(cid:2)2 xþ2 ix Copyright 2003 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.