1 , 0 0 1 A l g e b r a I P r a c t i c e P r o b l e m s FOR DUMmIES‰ by Mary Jane Sterling 1,001 Algebra I Practice Problems For Dummies® Published by John Wiley & Sons, Inc. 111 River St. Hoboken, NJ 07030-5774 www.wiley.com Copyright © 2013 by John Wiley & Sons, Inc., Hoboken, New Jersey Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada 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, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. 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Library of Congress Control Number: 2012956402 ISBN 978-1-118-44671-3 (pbk); ISBN 978-1-118-44665-2 (ebk); ISBN 978-1-118-44666-9 (ebk); ISBN 978-1-118-44669-0 (ebk) Manufactured in the United States of America 10 9 8 7 6 5 4 3 2 1 About the Author Mary Jane Sterling is the author of six For Dummies titles: Algebra I For Dummies, Algebra II For Dummies, Trigonometry For Dummies, Math Word Problems For Dummies, Business Math For Dummies, and Linear Algebra For Dummies. She has also written many supplementary workbooks and study aids. Mary Jane continues doing what she loves best: teaching mathematics. When not teaching or writing For Dummies books, she loves spending her time reading murder mysteries and fishing for her dinner. Dedication The author dedicates this book to her son, Sgt. James T. Sterling, USMC, and the other members of the 4th Air/Naval Gunfire Liaison Company, Det Juliet (part of Operation Enduring Freedom 2012). Jim and the others in his unit, as well as all military serving the U.S., have our utmost respect and appreciation. Author’s Acknowledgments The author issues a big thank you to project editor Tim Gallan, who has taken on the huge challenge of creating this new product. He has taken a lot of raw material and made it into this wonderful, finished workbook. Thank you so much for your hard work and patience. Also, a heartfelt thank you to the math editors, Suzanne Langebartels and Stephanie Long. As careful as I may be to do all the problems correctly, there is always that chance of a silly error. The editors keep me honest! And, of course, a grateful thank you to acquisitions editor Lindsay Lefevere, who again found me another interesting project. Publisher’s Acknowledgments We’re proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002. Some of the people who helped bring this book to market include the following: Acquisitions, Editorial, and Vertical Websites Composition Services Senior Project Editor: Tim Gallan Senior Project Coordinator: Kristie Rees Executive Editor: Lindsay Sandman Lefevere Layout and Graphics: Carrie A. Cesavice, Melissa Smith, Erin Zeltner Copy Editor: Suzanne Langebartels Proofreaders: Lindsay Amones, Debbye Butler Assistant Editor: David Lutton Indexer: Potomac Indexing, LLC Editorial Program Coordinator: Joe Niesen Technical Editor: Stephanie Long Editorial Manager: Michelle Hacker Editorial Assistants: Rachelle S. Amick, Alexa Koschier Publishing and Editorial for Consumer Dummies Kathleen Nebenhaus, Vice President and Executive Publisher David Palmer, Associate Publisher Kristin Ferguson-Wagstaffe, Product Development Director Publishing for Technology Dummies Andy Cummings, Vice President and Publisher Composition Services Debbie Stailey, Director of Composition Services Contents at a Glance Introduction ............................................................................1 Part I: The Questions ................................................................5 Chapter 1: Signing on with Signed Numbers .....................................................................................7 Chapter 2: Recognizing Algebraic Properties and Notation .........................................................13 Chapter 3: Working with Fractions and Decimals ..........................................................................17 Chapter 4: Making Exponential Expressions and Operations More Compatible........................23 Chapter 5: Raking in Radicals ............................................................................................................29 Chapter 6: Creating More User-Friendly Algebraic Expressions ..................................................35 Chapter 7: Multiplying by One or More Terms ...............................................................................41 Chapter 8: Dividing Algebraic Expressions .....................................................................................47 Chapter 9: Factoring Basics ...............................................................................................................53 Chapter 10: Factoring Binomials .......................................................................................................57 Chapter 11: Factoring Quadratic Trinomials ...................................................................................61 Chapter 12: Other Factoring Techniques ........................................................................................65 Chapter 13: Solving Linear Equations ..............................................................................................69 Chapter 14: Taking on Quadratic Equations ...................................................................................73 Chapter 15: Solving Polynomials with Powers Three and Higher ................................................79 Chapter 16: Reining in Radical and Absolute Value Equations .....................................................83 Chapter 17: Making Inequalities More Fair ......................................................................................87 Chapter 18: Using Established Formulas .........................................................................................93 Chapter 19: Using Formulas in Geometric Story Problems ...........................................................99 Chapter 20: Tackling Traditional Story Problems ........................................................................105 Chapter 21: Graphing Basics ...........................................................................................................111 Chapter 22: Using the Algebra of Lines ..........................................................................................117 Chapter 23: Other Graphing Topics ...............................................................................................121 Part II: The Answers ............................................................125 Chapter 24: Answers.........................................................................................................................127 Index ..................................................................................425