Intermediate Algebra For College Students

viii  Prefaceapplications include the percentage of the U.S. population using the Internet(Exercise Set 1.3, Exercises 47–52), taxes (Section 1.7 opener; Section 1.7, Example 5and Check Point 5), growing world population (Section 1.7, Example 3), support formarriage equality among Democrats and Republicans (Chapter 1 Review,Exercise 75), the number of U.S. prisoners (Chapter 1 Test, Exercise 8;Exercise Set 2.3, Exercises 63–65), U.S. births and deaths (Section 2.3 opener;Section 2.3, Example 5 and Check Point 5), overweight U.S. adults (Exercise Set 2.4,Exercises 85–86), the federal minimum wage (Exercise Set 2.4, Exercise 112),climate change (Chapter 2 Review, Exercise 60), employment, by gender(Exercise Set 3.1, Exercises 95–96), school bullying (Exercise Set 4.1, Exercises 57–58),diagnosed HIV cases (Section 5.1 opener), Amazon deforestation (Chapter 6Review, Exercise 91), and Americans giving up their citizenship, primarily for taxreasons (Exercise Set 11.1, Exercise 58). NEW! Animations created in GeoGebra help students visualize mathematical concepts through directed explorations and purposeful manipulation.Corresponding MyLab Math exercises allow these new animations to be assignedwith assessment to check for understanding. NEW! Integrated Review in MyLab Math can be used in a corequisite course orsimply to help students who enter their course without a full understanding ofprerequisite skills.Once the instructor has assigned the premade Integrated Review assignments, students begin each chapter by completing a Skills Check to pinpoint which prerequisite topics, if any, they need to review.Personalized review homework provides extra support for students who need it onjust the topics they did not master in the Skills Check.Additional review materials, including worksheets and videos, are available.What Familiar Features Have Been Retained in the EighthEdition of Intermediate Algebra for College Students? Learning Objectives. Learning objectives, framed in the context of a studentquestion (What am I supposed to learn?), are clearly stated at the beginning of eachsection. These objectives help students recognize and focus on the section’s mostimportant ideas. The objectives are restated in the margin at their point of use. Chapter-Opening and Section-Opening Scenarios. Every chapter and everysection open with a scenario presenting a unique application of mathematics instudents’ lives outside the classroom. These scenarios are revisited in the course ofthe chapter or section in an example, discussion, or exercise. Innovative Applications. A wide variety of interesting applications, supported byup-to-date, real-world data, are included in every section. Detailed Worked-Out Examples. Each example is titled, making the purpose ofthe example clear. Examples are clearly written and provide students with detailedstep-by-step solutions. No steps are omitted and each step is thoroughly explainedto the right of the mathematics. Explanatory Voice Balloons. Voice balloons are used in a variety of ways todemystify mathematics. They translate algebraic ideas into everyday English, helpclarify problem-solving procedures, present alternative ways of understandingconcepts, and connect problem solving to concepts students have already learned. Check Point Examples. Each example is followed by a similar matched problem,called a Check Point, offering students the opportunity to test their understandingof the example by working a similar exercise. The answers to the Check Points areprovided in the answer section. Concept and Vocabulary Checks. This feature offers short-answer exercises, mainlyfill-in-the-blank and true/false items, that assess students’ understanding of thedefinitions and concepts presented in each section. The Concept and VocabularyChecks appear as separate features preceding the Exercise Sets.A01 BLIT3700 08 AIE FM.indd 816/12/19 10:12 AM

Preface  ix Extensive and Varied Exercise Sets. An abundant collection of exercises isincluded in an Exercise Set at the end of each section. Exercises are organizedwithin eight category types: Practice Exercises, Practice Plus Exercises, ApplicationExercises, Explaining the Concepts, Critical Thinking Exercises, TechnologyExercises, Retaining the Concepts, and Preview Exercises. This format makes iteasy to create well-rounded homework assignments. The order of the PracticeExercises is exactly the same as the order of the section’s worked examples. Thisparallel order enables students to refer to the titled examples and their detailedexplanations to achieve success working the Practice Exercises. Practice Plus Problems. This category of exercises contains more challenging practiceproblems that often require students to combine several skills or concepts. With anaverage of ten Practice Plus problems per Exercise Set, instructors are provided with theoption of creating assignments that take Practice Exercises to a more challenging level. Mid-Chapter Check Points. At approximately the midway point in each chapter,an integrated set of Review Exercises allows students to review and assimilate theskills and concepts they learned separately over several sections. Graphing and Functions. Graphing is introduced in Chapter 1 and functions areintroduced in Chapter 2, with an integrated graphing functional approachemphasized throughout the book. Graphs and functions that model data appearin nearly every section and Exercise Set. Examples and exercises use graphs offunctions to explore relationships between data and to provide ways of visualizinga problem’s solution. Because functions are the core of this course, students arerepeatedly shown how functions relate to equations and graphs. Integration of Technology Using Graphic and Numerical Approaches to Problems.Side-by-side features in the technology boxes connect algebraic solutions tographic and numerical approaches to problems. Although the use of graphingutilities is optional, students can use the explanatory voice balloons to understanddifferent approaches to problems even if they are not using a graphing utility inthe course. Great Question! This feature presents a variety of study tips in the context ofstudents’ questions. Answers to questions offer suggestions for problem solving,point out common errors to avoid, and provide informal hints and suggestions.As a secondary benefit, this feature should help students not to feel anxious orthreatened when asking questions in class. Achieving Success. The Achieving Success boxes at the end of many sections offerstrategies for persistence and success in college mathematics courses. Chapter Review Grids. Each chapter contains a review chart that summarizes thedefinitions and concepts in every section of the chapter. Examples that illustratethese key concepts are also included in the chart. End-of-Chapter Materials. A comprehensive collection of Review Exercises foreach of the chapter’s sections follows the review grid. This is followed by a ChapterTest that enables students to test their understanding of the material covered in thechapter. Beginning with Chapter 2, each chapter concludes with a comprehensivecollection of mixed Cumulative Review Exercises. Blitzer Bonuses. These enrichment essays provide historical, interdisciplinary, andotherwise interesting connections to the algebra under study, showing students thatmath is an interesting and dynamic discipline. Discovery. Discover for Yourself boxes, found throughout the text, encourage studentsto further explore algebraic concepts. These explorations are optional and theiromission does not interfere with the continuity of the topic under consideration.I hope that my passion for teaching, as well as my respect for the diversity ofstudents I have taught and learned from over the years, is apparent throughout thisnew edition. By connecting algebra to the whole spectrum of learning, it is my intent toshow students that their world is profoundly mathematical, and indeed, p is in the sky.Robert BlitzerA01 BLIT3700 08 AIE FM.indd 916/12/19 10:12 AM

Get the most out ofMyLab MathMyLab Math for Intermediate Algebra for College Students, by Bob Blitzer(access code required)Bob Blitzer’s Intermediate Algebra for College Students offers market-leading content tightlyintegrated with the #1 choice in digital learning—MyLab Math. MyLab Math courses can betailored to the needs of instructors and students, while weaving the Blitzer’s distinct, relatablevoice into all elements of the course.Support StudentsWherever, WheneverA wealth of video resources providesstudents with extra help for each sectionof text. Check Point Videos showinstructors working out each CheckPoint problem in the section to ensureunderstanding. Section Lecture Videoscover important topics from key sectionsto provide students with extra help.Motivate with Real-WorldApplicationsAnimated Blitzer Bonus videos mirror thispopular feature from the text. Blitzer Bonusvideos use the author’s signature style tohelp students connect mathematical topicsto the world around them. Correspondingassignable exercises in MyLab Mathallow these videos to be assigned for creditand check student understanding, whileengaging them through an application.pearson.com/mylab/mathxA01 BLIT3700 08 AIE FM.indd 1016/12/19 10:12 AM

Get the most out ofMyLab MathGet Students PreparedNEW! Integrated Review can be used in a corequisite course or simply to help students whoenter their course without a full understanding of prerequisite skills. O nce the instructor has assigned the premade Integrated Review assignments, students begineach chapter by completing aSkills Check to pinpoint whichtopics, if any, they need to review. Personalized review homeworkprovides extra support forstudents who need it on just thetopics they did not master in theSkills Check. Additional review materials,including worksheets and videos, are available.Encourage Conceptual UnderstandingNEW! Animations created in GeoGebra help students visualize mathematical conceptsthrough directed explorations and purposeful manipulation. Corresponding MyLab Mathexercises allow these new animations tobe assigned with assessment to check forunderstanding.Foster College SuccessNEW! A Mindset module includesgrowth-mindset videos and exercises thatencourage students to maintain a positiveattitude about learning, value their ownability to grow, and view mistakes as alearning opportunity.pearson.com/mylab/mathA01 BLIT3700 08 AIE FM.indd 1116/12/19 10:12 AM

Resources forSuccessInstructor ResourcesStudent ResourcesAnnotated Instructor’s EditionLearning GuideAnswers to exercises are printed on the same textpage with longer answers at the back of the text.The Learning Guide helps students learn howto make the most of their textbook, while alsoproviding additional practice for each section andguidance for test preparation. This workbookincludes activities intended for group work inclass to help students put the math intoreal-world context. The Learning Guide alsoincludes Integrated Review Worksheets that canbe used in conjunction with the Integrated Reviewobjectives in the MyLab course. The LearningGuide is published in an unbound, binder-readyformat so that it can serve as the basis for acourse notebook.Additional resources can be downloaded fromwww.pearsonhighered.com or found in theInstructor Resources area of the MyLab Mathcourse.Instructor’s Resource Manual withTests and Mini-LecturesIncludes mini-lectures for each text section,additional practice worksheets for each section,several forms of tests per chapter—free responseand multiple choice, and answers to all items.Instructor’s Solutions ManualIncludes fully worked solutions to every exercise inthe text.TestGen Enables instructors to build, edit, print, andadminister tests using a computerized bank ofquestions developed to cover all the objectives ofthe text. TestGen is algorithmically based, allowinginstructors to create multiple but equivalentversions of the same question or test with the clickof a button. Instructors can also modify test bankquestions or add new questions.Student Solutions ManualProvides completely worked-out solutions tothe odd-numbered section exercises and allexercises in the Integrated Reviews, ChapterReviews, Chapter Tests, and Cumulative Reviews.Video SeriesThese videos, available in MyLab Math, providestudents with extra help for key sections of thetextbook.PowerPoint Lecture SlidesFully editable slides correlated with the textbookinclude definitions, key concepts, and examples.Accessible versions of the PowerPoints are alsoavailable in the course.pearson.com/mylab/mathA01 BLIT3700 08 AIE FM.indd 1216/12/19 10:12 AM

Preface  xiiiAcknowledgmentsAn enormous benefit of authoring a successful series is the broad-based feedbackI receive from the students, dedicated users, and reviewers. Every change to thisedition is the result of their thoughtful comments and suggestions. I would like toexpress my appreciation to all the reviewers, whose collective insights form thebackbone of this revision. In particular, I would like to thank the following peoplefor reviewing Intermediate Algebra for College Students.Cindy Adams, San Jacinto CollegeGwen P. Aldridge, Northwest MississippiCommunity CollegeRonnie Allen, Central New MexicoCommunity CollegeDr. Simon Aman, Harry S. TrumanCollegeHoward Anderson, Skagit Valley CollegeJody Anderson, Angelina CollegeJohn Anderson, Illinois ValleyCommunity CollegeDeborah Detrick, Kansas City KansasCommunity CollegeJill DeWitt, Baker College of MuskegonBen Divers, Jr., Ferrum CollegeCynthia Dominguez, Los Angeles TradeTechnical CollegeIrene Doo, Austin Community CollegeCharles C. Edgar, Onondaga CommunityCollegeMichael H. Andreoli, Miami-DadeCollege – North CampusMichele Bach, Kansas City KansasCommunity CollegeAnna Bakman, Los Angeles TradeTechnical CollegeElise Fischer, Johnson CountyCommunity CollegeJana Barnard, Angelo State UniversityRochelle Beatty, Kansas City KansasCommunity CollegeRosanne Benn, Prince George’sCommunity CollegeRenee Boggan, East CentralCommunity CollegeChristine Brady, Suffolk CountyCommunity CollegeGale Brewer, Amarillo CollegeCarmen Buhler, Minneapolis Community& Technical CollegeWarren J. Burch, Brevard CollegeAlice Burstein, Middlesex CommunityCollegeEdie Carter, Amarillo CollegeJerry Chen, Suffolk County CommunityCollegeSandra Pryor Clarkson, Hunter CollegeSally Copeland, Johnson CountyCommunity CollegeValerie Cox, Calhoun Community CollegeCarol Curtis, Fresno City CollegeRobert A. Davies, Cuyahoga CommunityCollegeA01 BLIT3700 08 AIE FM.indd 13Karen Edwards, Diablo Valley CollegeScott Fallstrom, MiraCosta CollegeSusan Forman, Bronx Community CollegeWendy Fresh, Portland CommunityCollegeJennifer Garnes, Cuyahoga CommunityCollegeGary Glaze, Eastern WashingtonUniversityJay Graening, University of ArkansasRobert B. Hafer, Brevard CollegeAndrea Hendricks, Georgia PerimeterCollegeDonald Herrick, Northern IllinoisUniversityBeth Hooper, Golden West CollegeSandee House, Georgia Perimeter CollegeTracy Hoy, College of Lake CountyLaura Hoye, Trident Community CollegeMargaret Huddleston, Schreiner UniversityLori James, University of CharlestonMarcella Jones, Minneapolis Community& Technical CollegeShelbra B. Jones, Wake TechnicalCommunity CollegeSharon Keenee, Georgia Perimeter CollegeRegina Keller, Suffolk CountyCommunity CollegeGary Kersting, North Central MichiganCollege16/12/19 10:12 AM

xiv  PrefaceDennis Kimzey, Rogue Community CollegeMatthew Peace, Florida Gateway CollegeKandace Kling, Portland CommunityCollegeDr. Bernard J. Piña, New Mexico StateUniversity – Doña Ana CommunityCollegeGray Knippenberg, Lansing CommunityCollegeJill Rafael, Sierra CollegeMary Kochler, Cuyahoga CommunityCollegeJames Razavi, Sierra CollegeScot Leavitt, Portland Community CollegeRobert Leibman, Austin CommunityCollegeJennifer Lempke, North Central MichiganCollegeAnn M. Loving, J. Sargent ReynoldsCommunity CollegeKent MacDougall, Temple CollegeJean-Marie Magnier, SpringfieldTechnical Community CollegeHank Martel, Broward CollegeKim Martin, Southeastern Illinois CollegeJohn Robert Martin, Tarrant CountyCollegeLisa McMillen, Baker College of AuburnHillsIrwin Metviner, State University of NewYork at Old WestburyJean P. Millen, Georgia Perimeter CollegePam Miller, Phoenix CollegeLawrence Morales, Seattle CentralCommunity CollegeMorteza Shafii-Mousavi, IndianaUniversity South BendLois Jean Nieme, MinneapolisCommunity & Technical CollegeAllen R. Newhart, ParkersburgCommunity CollegeKaren Pain, Palm Beach State CollegePeg Pankowski, Community College ofAllegheny County – South CampusRobert Patenaude, College of the CanyonsChristopher Reisch, The State Universityof New York at BuffaloGeorge Reed, Angelina CollegeNancy Ressler, Oakton Community CollegeKatalin Rozsa, Mesa Community CollegeHaazim Sabree, Georgia PerimeterCollegeChris Schultz, Iowa State UniversityShannon Schumann, University of PhoenixLiz Scott, Angelina CollegeBarbara Sehr, Indiana UniversityKokomoBrian Smith, Northwest ShoalsCommunity CollegeGayle Smith, Lane Community CollegeTanya M. Smith, Kansas City KansasCommunity CollegeDick Spangler, Tacoma CommunityCollegeJanette Summers, University of ArkansasRobert Thornton, Loyola UniversityLucy C. Thrower, Francis MarionCollegeMary Thurow, Minneapolis Community &Technical CollegeRichard Townsend, North CarolinaCentral UniversityCindie Wade, St. Clair CountyCommunity CollegeAndrew Walker, North SeattleCommunity CollegeKathryn Wetzel, Amarillo CollegeAdditional acknowledgments are extended to Dan Miller and Dan Richbart forpreparing the solutions manuals and the Learning Guide; Brad Davis, for preparingthe answer section and serving as accuracy checker; Brian Morris at ScientificIllustrators, for superbly illustrating the book; and Francesca Monaco, projectmanager, and Kathleen Manley, production editor, whose collective talents kept everyaspect of this complex project moving through its many stages.I would like to thank my editors at Pearson, Dawn Murrin, Mary Vann, andKayla Shearns, who guided and coordinated the book from manuscript throughproduction. Thanks to Studio Montage for the quirky cover. Finally, thanks tomarketing manager Alicia Wilson for your innovative marketing efforts, and to theentire Pearson sales force, for your confidence and enthusiasm about the book.A01 BLIT3700 08 AIE FM.indd 1416/12/19 10:12 AM

To the StudentThe bar graph shows some of the qualities that students say make a great teacher.Q UALExplainITIESs thingT H ATs clearlyMAKEA GREFunny and entertainingHelpfulAT T E ACHER70%47%Passiotheir s nate aboutubjec t40%22%10%Source:Avanta Learning System30%50%70%It was my goal to incorporate each of the qualities that make a great teacherthroughout the pages of this book.Explains Things ClearlyI understand that your primary purpose in reading Intermediate Algebra for CollegeStudents is to acquire a solid understanding of the required topics in your algebracourse. In order to achieve this goal, I’ve carefully explained each topic. Importantdefinitions and procedures are set off in boxes, and worked-out examples that presentsolutions in a step-by-step manner appear in every section. Each example is followedby a similar matched problem, called a Check Point, for you to try so that you canactively participate in the learning process as you read the book. (Answers to allCheck Points appear in the back of the book.)xvA01 BLIT3700 08 AIE FM.indd 1516/12/19 10:12 AM

xvi  To the StudentFunny/EntertainingWho says that an algebra textbook can’t be entertaining? From our quirky cover tothe photos in the chapter and section openers, prepare to expect the unexpect

succeed in intermediate algebra. Intermediate Algebra for College Students, Eighth Edition, has two primary goals: 1. To help students acquire a solid foundation in the skills and concepts of intermediate algebra needed for success in future STEM and non-STEM directed math courses. 2. To show students how