Elementary Algebra - Pearson

Sample Preface. Not for Distribution.PrefaceWelcome to the 10th edition of Elementary Algebra forCollege Students! This book has been used by thousandsof students and other adults who have never been exposedto algebra or those who have been exposed but need arefresher course. Our primary goal was to write a book thatstudents can read, understand, and enjoy. To achieve thisgoal we have used short sentences, clear explanations,and many detailed, worked-out examples. We have tried tomake the book relevant to college students by using practical applications of algebra throughout the text. The MyLab Math course itself includes extensiveenhancements to improve outcomes for students:–– The addition of Skillbuilder exercises–– The addition of Workspace assignments–– Author-developed Sample Assignments thatinstructors can assign to utilize all of the newexercise enhancements–– Learning Catalytics questions for each chapter–– Fully accessible PowerPoint slidesNew to This EditionFeatures of the TextOne of the most important features of the text is its emphasis on readability. The book is very understandableto students at all reading skill levels. The Tenth Editionretains this emphasis and has been revised with a focuson improving accessibility and addressing the learningneeds and styles of today’s students. To this end, the following changes have been made:AccuracyContent Changes We’ve done an extensive review of exercise sets,including an analysis of data analytics on exerciseusage, leading to modification of exercises and exercise sets as follows:–– Exercise sets have been modified to ensure precise graduation from simple to more complex andinclude more direct matching of the book examplesand the corresponding exercises in MyLab Math.This creates a better experience throughout forstudents as well as making the material in the bookbetter connected to the homework students do.–– Precise correlation has been made between eachodd and even exercise. The odds can be used asexamples and solutions are provided, and the evenscan be assigned as homework or in MyLab Math.–– Now Try Exercises are revised, with particularfocus on odd–even pairing. Chapter openers each include a new video, createdby the authors, that explains how the material presented in the chapter is used to solve problems fromeveryday life. These explanations are carried into theactual solution to one or more exercises that are inthe chapter and to other assignable exercises. Renewed focus on the Understanding Algebra feature throughout the book. Many UnderstandingAlgebra boxes are new or revised for greater clarity.The new design of the Understand Algebra boxes willmake them stand out more.Accuracy in a mathematics text is essential. To ensureaccuracy in this book, math teachers from around thecountry have read the pages carefully for typographicalerrors and have checked all the answers.Making ConnectionsMany of our students do not thoroughly grasp new concepts the first time they are presented. In this text weencourage students to make connections. That is, weintroduce a concept, then later in the text briefly reintroduce it and build upon it. Often an important conceptis used in many sections of the text. Important conceptsare also reinforced throughout the text in the CumulativeReview Exercises and Cumulative Review Tests.Chapter Opening ApplicationEach chapter begins with a real-life application relatedto the material covered in the chapter and further illuminated through an author created video explanationwithin MyLab Math. By the time students complete thechapter, they should have the knowledge to work theproblem.Goal of This ChapterThis feature on the chapter opener page gives studentsa preview of the chapter and also indicates where this material will be used again in other chapters of the book.This material helps students see the connections amongvarious topics in the book and the connection to realworld situations.Keyed Section ObjectivesEach section opens with a list of skills that the studentshould learn in that section. The objectives are thenkeyed to the appropriate portions of the sections withblue numbers such as 1 .xiiiA01 RUND6539 10 AIE FM.indd 1311/3/17 5:23 PM

xivPrefaceSample Preface. Not for Distribution.Problem SolvingPólya’s five-step problem-solving procedure is discussedin Section 1.2. Throughout the book, problem solvingand Pólya’s problem-solving procedure are emphasized.Practical ApplicationsPractical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. Theproblem- solving approach used throughout this text givesstudents ample practice in setting up and solving application problems. The use of practical applicationsmotivates students.Detailed, Worked-Out ExamplesA wealth of examples have been worked out in a step-bystep, detailed manner. Important steps are highlightedin color, and no steps are omitted until after the studenthas seen a sufficient number of similar examples.Now Try ExercisesIn each section, after each example, students are askedto work an exercise that parallels the example given inthe text. These Now Try Exercises make the students active, rather than passive, learners and they reinforce theconcepts as students work the exercises. Through theseexercises, students have the opportunity to immediatelyapply what they have learned. After each example,Now Try Exercises are indicated in orange type such asNow Try Exercise 27 . They are also indicated in green typein the exercise sets, such as 27.Study Skills SectionStudents taking this course may benefit from a review ofessential study skills. Such study skills are essential forsuccess in mathe matics. Section 1.1, the first section ofthe text, discusses such study skills. This section shouldbe very beneficial for your s tudents and should helpthem to achieve success in mathematics.Understanding AlgebraUnderstanding Algebra boxes appear in the margin throughout the text. Placed at key points, Understanding Algebraboxes help students focus on the important concepts andfacts that they need to master.Helpful HintsThe Helpful Hint boxes offer useful suggestions forproblem solving and other varied topics. They are setoff in a special manner so that students will be sure toread them.Avoiding Common ErrorsCommon student errors are illustrated. Explanationsof why the shown procedures are incorrect are given.Explanations of how students may avoid such errors arealso presented.A01 RUND6539 10 AIE FM.indd 14Exercise SetsThe exercise sets are broken into three main categories:Warm-Up Exercises, Practice the Skills, and ProblemSolving. Many exercise sets also contain Concept/WritingExercises, Challenge Problems, and/or Group Activities.Each exercise set is graded in difficulty, and the exercises are paired. The early problems help develop thestudents’ confidence, and then students are eased gradually into the more difficult problems. A sufficient number and variety of examples are given in each section forstudents to successfully complete even the more difficultexercises. The number of exercises in each section ismore than ample for student assignments and practice.Warm-Up ExercisesThe exercise sets begin with Warm-Up Exercises. Thesefill-in-the-blank exercises include an emphasis on vo cabulary. They serve as a great warm-up to the homeworkexercises or as 5-minute quizzes.Practice the Skills ExercisesThe Practice the Skills exercises reinforce the conceptsand procedures discussed in the section. These exercisesprovide students with practice in working problems similar to the examples given in the text. In many sectionsthe Practice the Skills exercises are the main and mostimportant part of the exercise sets.Problem-Solving ExercisesThese exercises help students become better thinkersand problem solvers. Many of these exercises involvereal-life applications of algebra. It is important for students to be able to apply what they learn to real-life situations. Many problem-solving exercises help with this.Concept/Writing ExercisesMost exercise sets include exercises that require students to write out the answers in words. These exercisesimprove students’ understanding and comprehension ofthe material. Many of these exercises involve problemsolving and conceptualization and help develop betterreasoning and critical thinking skills.Challenge ProblemsThese exercises, which are part of many exercise sets,provide a variety of problems. Many were written tostimulate student thinking. Others provide additionalapplications of algebra or present material from futuresections of the book so that s tudents can see and learnthe material on their own before it is covered in class.Others are more challenging than those in the regularexercise set.Group ActivitiesMany exercise sets have Group Activity exercises thatlead to interesting group discussions. Many students11/3/17 5:23 PM

Sample Preface. Not for Distribution.learn well in a cooperative learning atmosphere, andthese exercises will get students talking mathematics toone another.Cumulative Review ExercisesAll exercise sets (beginning with Section 1.3) containquestions from previous sections in the chapter and fromprevious chapters. These Cumulative Review Exerciseswill reinforce topics that were previously covered andhelp students retain the earlier material while they arelearning the new material. For the students’ benefit,Cumulative Review Exercises are keyed to the sectionwhere the material is covered, using brackets, suchas [3.4].Mid-Chapter TestsIn the middle of each chapter is a Mid-Chapter Test.Students should take each Mid-Chapter Test to makesure they understand the material presented in the chapter up to that point. In the student answers, bracketssuch as [2.3] are used to indicate the section where thematerial was first presented.Chapter SummaryAt the end of each chapter is a comprehensive chaptersummary that includes important chapter facts and examples illustrating these important facts.Chapter Review ExercisesAt the end of each chapter are review exercises thatcover all types of exercises presented in the chapter. Thereview exercises are keyed using colored numbers andbrackets, such as [1.5], to the sections where the material was first introduced.Chapter Practice TestsThe comprehensive end-of-chapter practice tests enable students to see how well they are prepared for theactual class test. The section where the material wasfirst introduced is indicated in brackets in the studentanswers.Cumulative Review TestsThese tests, which appear at the end of each chapterafter the first, test the students’ knowledge of materialA01 RUND6539 10 AIE FM.indd 15Prefacexvfrom the beginning of the book to the end of that chapter. Students can use these tests for review, as well asfor preparation for the final exam. These exams, like theCumulative Review Exercises, serve to reinforce topicstaught earlier. In the answer section, after each answer,the section where that material was covered is given using brackets.AnswersThe odd-numbered answers are provided for the exercise sets. All answers are provided for the CumulativeReview Exercises, Mid-Chapter Test, Chapter ReviewExercises, Chapter Practice Tests, and CumulativeReview Tests. Answers are not provided to students forthe Group Activity exercises because we want studentsto reach agreement by themselves on the answers tothese exercises.PrerequisiteThis text assumes no prior knowledge of algebra.However, a working knowledge of arithmetic skills isimportant. Fractions are reviewed early in the text, anddecimals and percent are reviewed in Appendix A.Modes of InstructionThe format and readability of this book, and its manyresources and supplements, lend it to many differentmodes of instruction. The constant reinforcement of concepts will result in greater understanding and retentionof the material by your students.The features of the text and its supplements make itsuitable for many types of instructional modes, including: face-to-face courseshybrid or blended coursesemporium-based coursesonline instructionaccelerated coursesself-paced instructioninverted classroomscooperative or group study11/3/17 5:23 PM

Sample Preface. Not for Distribution.Resources for SuccessGet the Most out of MyLab Math forElementary Algebra, Tenth Editionby Allen Angel and Dennis RundeThe Angel/Runde team has helped thousands of students learn algebra throughclear examples and concise language. With this revision, the authors have continued their hallmark clear writing style. This, along with new media resources andrevamped exercise sets, provides students with a comprehensive learning andpractice environment in MyLab Math. Bringing the authors’ voice and approachinto the MyLab course gives students the motivation, understanding, and skill setthey need to master algebra.Take advantage of the following resources to get the most out of your MyLabMath course.Support and Motivate with Video ResourcesNEW! Chapter Opener Videos highlight how the math students are about to learn can be applied and used in the real world. Providing an interesting and useful overview of the chapter,these videos can be assigned or even used in the classroom to kick off a lecture.Instructional Videos walk students through conceptsand examples in a modern presentation format. Videosare accessible in many ways, including from the eTextpages and from within homework e xercises and canalso be assigned in a media assignment to encouragestudents to watch them. All videos can be played fromany laptop or mobile device to provide support even onthe go.Chapter Test Prep Videos help students during their most teachable moment—when they arepreparing for a test. The videos provide step-by-step solutions for every exercise found in thetext’s Chapter Tests.pearson.com/mylab/mathA01 RUND6539 10 AIE FM.indd 1611/3/17 5:23 PM

Sample Preface. Not for Distribution.Personalize Students’ LearningOne size does not fit all, especially when it comes to developmental math students. Instructorshave the option to personalize students’ experiences in the MyLab course with new tools, including personalized homework and Skill Builder.Personalized Homeworkdelivers assignments tostudents tailored to theirunderstanding of topicsbased on their performance on a test or quiz.This way, students canfocus on just the topicsthey have not yet masteredand receive credit for thetopics they mastered onthe quiz or test.New! Skill Builderassignments offer justin-time adaptive practice.The adaptive engine tracksstudent performanceand delivers questionsto each individual thatadapt to his or her level ofunderstanding.This newfeature allows instructorsto assign fewer questionsfor homework, allowingstudents to complete asmany or as few questionsneeded.Build Your Course More EasilyEnhanced Sample Assignments make course setup easier by giving instructors a starting point foreach chapter. Each assignment has been carefully curated for this specific text by author DennisRunde based on his and his students’ experiences with MyLab Math and has been crafted to includea thoughtful mix of question types.pearson.com/mylab/mathA01 RUND6539 10 AIE FM.indd 1711/3/17 5:23 PM

Sample Preface. Not for Distribution.Student and Instructor ResourcesSTUDENT RESOURCESStudent Solutions ManualProvides complete worked-out solutions to the odd-numbered section exercises all exercises in the Mid-Chapter Tests, ChapterReviews, Chapter Practice Tests, and CumulativeReview TestsISBN: 978-0-13-476651-5Student Workbook Extra practice exercises for every section of thetext with ample space for students to show theirworkISBN: 978-0-13-476659-1Video ProgramThe Angel/Runde video program, available through MyLab Math, includes: Objective-based videos Example-based videos covering most examples and related end of section exericses Chapter Test Prep videos that offer step-by-step solutions to exercises in Chapter Tests Videos are captioned, and can be viewed on any mobile deviceINSTRUCTOR RESOURCESAnnotated Instructor’s EditionContains all the content found in the student edition,plus the following: Answers to exercises on the same text page withgraphing answers in the Graphing Answer sectionat the back of the text Instructor Example provided in the margin pairedwith each student exampleInstructor’s Resource Manual with Testsand Mini-Lectures Mini-lectures for each text section Several forms of test per chapter (free responseand multiple choice) Answers to all items Available for download from the IRC and inMyLab MathInstructor’s Solutions Manual Provides complete worked-out solutions to allsection exercises Available for download from the IRC andin MyLab MathTestGen Enables instructors to build, edit, print, andadminis ter tests using a computerized bank ofquestions developed to cover all the objectives ofthe text. Algorithmically based, allowing instructors to create multiple but equivalent versions of thesame question or test with the click of a button;instructors can also modify test bank questionsor add new questions.MyLab Math Online Course (access code required)MyLab Math is the world’s leading homework, tutorial, and assessment program. It creates personalizedlearning experiences for students and provides powerful tools for instructors. Learn more about MyLab Mathat pearson.com/mylab/math.xviiiA01 RUND6539 10 AIE FM.indd 1811/3/17 5:23 PM

Sample Preface. Not for Distribution.AcknowledgmentsWe thank our spouses, Kathy Angel and Kris Runde, fortheir support and encouragement throughout the project.We are grateful for their wonderful support and understanding while we worked on the book.We also thank our children: Robert and Steven Angeland Alex, Nick, and Max Runde. They also gave us supportand encouragement and were very understanding when wecould not spend as much time with them as we wished because of book deadlines. Special thanks to daughter-in-law,Kathy; mother-in-law, Patricia; and father-in-law, Scott.Without the support and understanding of our families, thisbook would not be a reality.We want to thank Joan Saniuk, Theresa Schille, SujathaThiru vengadathan, and Cathleen Zucco-Teveloff for accuracy reviewing the pages and checking all answers.Many people at Pearson deserve thanks, includingall those listed on the copyright page. In particular,we thank Michael Hirsch, Editor-in-Chief; Rachel Reeve,Content Producer; Shannon Bushee, Editorial Assistant;Shana Siegmund, Producer; Eric Gregg, Senior ContentDeveloper; Alicia Frankel, Product Marketing Manager; andHanna Lafferty, Product Marketing Assistant.We would like to thank the following reviewers andfocus group participants of this Tenth Edition (marked withan asterisk) and recent editions for their thoughtful comments and suggestions.Darla Aguilar, Pima Community College, AZFrances Alvarado, University of Texas–PanAmerican, TXJose Alvarado, University of Texas–Pan American, TXBen Anderson, Darton College, GALinda Barton, Ball State, INElizabeth Bonawitz, University of Rio Grande, OHSharon Berrian, Northwest Shoals CommunityCollege, ALDianne Bolen, Northeast Mississippi CommunityCollege, MSJulie Bonds, Sonoma State University, CAClark Brown, Mojave Community College, AZConnie Buller, Metropolitan Community College, NEMarc D. Campbell, Daytona State College, FLJulie Chesser, Owens Community College, OHKim Christensen, Maple Woods Community College, MOBarry Cogan, Macomb Community College, MIPat C. Cook, Weatherford College, TXOlga Cynthia Harrison, Baton Rouge CommunityCollege, LALisa DeLong Cuneo, Pennsylvania State University–Dobois, PAStephan Delong, Tidewater Community College, VA*Deborah Doucette, Erie Community College (North), NYWilliam Echols, Houston Community College, TXKaren Egedy, Baton Rouge Community College, LAA01 RUND6539 10 AIE FM.indd 19PrefacexixJanet Evert, Erie Community College (South), NYDaniel Fahringer, Harrisburg Area CommunityCollege, PADale Felkins, Arkansas Technical University, AR*Ernie Forgione, Centra

7 Graphing Linear Equations 437 17. The Cartesian Coordinate System and Linear Equations in Two Variables 438 7.2 Graphing Linear Equations 445 7.3 Slope of a Line 455 Mid-Chapter Test: Sections 7.1–7.3 465 47. Slope-Intercept and Point-Slope Forms of a Linear Equation 466 7.5 Graphing Linear Inequalities 478 7.6 Functions 483