Elementary And Intermediate Algebra
Sample Preface. Not for Distribution.ANNOTATED INSTRUCTOR’S EDITIONElementary andIntermediate Algebrafor College Students5eAllen R. AngelMONROE COMMUNITY COLLEGEDennis C. RundeSTATE COLLEGE OF FLORIDAA01 RUND5089 05 AIE FM.indd 11/6/18 8:06 PM
Sample Preface. Not for Distribution.Editorial Director: Chris HoagEditor in Chief: Michael HirschEditorial Assistant: Shannon BusheeContent Producer: Rachel S. ReeveManaging Producer: Scott DisannoProducer: Shana SiegmundManager, Courseware QA: Mary DurnwaldManager, Content Development: Eric GreggProduct Marketing Manager: Alicia FrankelField Marketing Managers: Jennifer Crum and Lauren SchurMarketing Assistant: Brooke ImbornoneSenior Author Support/Technology Specialist: Joe VetereManager, Rights and Permissions: Gina CheselkaManufacturing Buyer: Carol Melville, LSC CommunicationsProduction Coordination, Composition, and Illustrations: IntegraCover and Text Design: Studio MontageCover Image: Kathryn Harris/4Goodnesscake/Moment/Getty Images (Cake);Constantin Stanciu/Shutterstock (Blackboard Labels)Copyright 2019, 2015, 2011 by Pearson Education, Inc. All Rights Reserved. Printed in theUnited States of America. This publication is protected by copyright, and permission should beobtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,or transmission in any form or by any means, electronic, mechanical, photocopying, recording,or otherwise. For information regarding permissions, request forms and the appropriatecontacts within the Pearson Education Global Rights & Permissions department, please visitwww.pearsoned.com/permissions/.Attributions of third party content appear on page P1-P3, which constitutes an extension of thiscopyright page.This work is protected by United States copyright laws and isprovided solely for the use ofinstructors in teaching theircourses and assessing studentlearning. Dissemination or saleof any part of this work(including on the World WideWeb) will destroy the integrityof the work and is not permitted. The work and materialsfrom it should never be madeavailable to students except byinstructors using the accompanying text in their classes. Allrecipients of this work areexpected to abide by theserestrictions and to honor theintended pedagogical purposes and the needs of otherinstructors who rely on thesematerials.PEARSON, ALWAYS LEARNING, and MYLAB are exclusive trademarks owned by PearsonEducation, Inc. or its affiliates in the U.S. and/or other countries.Unless otherwise indicated herein, any third-party trademarks that may appear in this workare the property of their respective owners and any references to third-party trademarks, logosor other trade dress are for demonstrative or descriptive purposes only. Such references arenot intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’sproducts by the owners of such marks, or any relationship between the owner and PearsonEducation, Inc. or its affiliates, authors, licensees or distributors.This work is solely for the use of instructors and administrators for the purpose of teaching coursesand assessing student learning. Unauthorized dissemination, publication or sale of the work, inwhole or in part (including posting on the internet) will destroy the integrity of the work and isstrictly prohibited.Library of Congress Cataloging-in-Publication DataThis book has been cataloged with the Library of CongressAnnotated Instructor’s EditionISBN 10:0-13-479508-3ISBN 13:978-0-13-479508-9Student EditionISBN 10:0-13-475894-3ISBN 13:978-0-13-475894-7A01 RUND5089 05 AIE FM.indd 21/6/18 8:06 PM
Sample Preface. Not for Distribution.To my brother, JerryAllen R. AngelTo my brothers and sisters,Nancy, Steve, Cathy, Rod, and Mary JoAnd to the memory of DaveDennis C. RundeA01 RUND5089 05 AIE FM.indd 31/6/18 8:06 PM
Sample Preface. Not for Distribution.Brief Contents1Real Numbers12Solving Linear Equations983Applications of Algebra1764Graphing Linear Equations5Exponents and Polynomials6Factoring7Rational Expressions and Equations8Functions and Their Graphs9Systems of Linear Equations23128034340648155310 Inequalities in One and Two Variables 62611 Roots, Radicals, and Complex Numbers12 Quadratic Functions74013 Exponential and Logarithmic Functions14 Conic Sections66882689715 Sequences, Series, and the Binomial Theorem941ivA01 RUND5089 05 AIE FM.indd 41/6/18 8:06 PM
Sample Preface. Not for Distribution.ContentsPreface xiTo the Student 1Real Numbers 1.11.21.31.41.5Study Skills for Success in MathematicsProblem Solving 7Fractions 21The Real Number System 35Inequalities and Absolute Value 41xix12Mid-Chapter Test: Sections 1.1–1.5 461.61.71.81.91.10Addition of Real Numbers 47Subtraction of Real Numbers 55Multiplication and Division of Real Numbers 66Exponents, Parentheses, and the Order of OperationsProperties of the Real Number System 83Chapter 1 Summary 89Chapter 1 Review Exercises 94Chapter 1 Practice Test 972Solving Linear Equations 74982.1 Combining Like Terms 992.2 The Addition Property of Equality 1082.3 The Multiplication Property of Equality 1152.4 Solving Linear Equations with a Variable on Only One Side of theEquation 122Mid-Chapter Test: Sections 2.1–2.4 1302.5 Solving Linear Equations with the Variable on Both Sides of theEquation 1312.6 Formulas 1412.7 Ratios and Proportions 155Chapter 2 Summary 168Chapter 2 Review Exercises 172Chapter 2 Practice Test 175Cumulative Review Test 1753Applications of Algebra 1763.1 Changing Application Problems into Equations3.2 Solving Application Problems 191177Mid-Chapter Test: Sections 3.1–3.2 2023.3 Geometric Problems 2033.4 Motion, Money, and Mixture Problems210vA01 RUND5089 05 AIE FM.indd 51/6/18 8:06 PM
viContentsSample Preface. Not for Distribution.Chapter 3 Summary 223Chapter 3 Review Exercises 225Chapter 3 Practice Test 228Cumulative Review Test 2294Graphing Linear Equations 2314.1 The Cartesian Coordinate System and Linear Equations in Two Variables 2324.2 Graphing Linear Equations 2404.3 Slope of a Line 251Mid-Chapter Test: Sections 4.1–4.3 2614.4 Slope-Intercept and Point-Slope Forms of a Linear EquationChapter 4 Summary 274Chapter 4 Review Exercises 276Chapter 4 Practice Test 278Cumulative Review Test 2785262Exponents and Polynomials 2805.1 Exponents 2815.2 Negative Exponents 2925.3 Scientific Notation 302Mid-Chapter Test: Sections 5.1–5.3 3115.4 Addition and Subtraction of Polynomials5.5 Multiplication of Polynomials 3195.6 Division of Polynomials 330Chapter 5 Summary 337Chapter 5 Review Exercises 339Chapter 5 Practice Test 341Cumulative Review Test 3423126Factoring ga Monomial from a Polynomial 344by Grouping 352Trinomials of the Form ax2 bx c, a 1 358Trinomials of the Form ax2 bx c, a Z 1 365Mid-Chapter Test: Sections 6.1–6.4 3766.5 Special Factoring Formulas and a General Review of Factoring6.6 Solving Quadratic Equations Using Factoring 3856.7 Applications of Quadratic Equations 391Chapter 6 Summary 399Chapter 6 Review Exercises 402Chapter 6 Practice Test 404Cumulative Review Test 4057377Rational Expressions and Equations 4067.1 Simplifying Rational Expressions 4077.2 Multiplication and Division of Rational Expressions 4147.3 Addition and Subtraction of Rational Expressions with a CommonDenominator and Determining the Least Common Denominator 423A01 RUND5089 05 AIE FM.indd 61/6/18 8:06 PM
ContentsSample Preface. Not for Distribution.7.4 Addition and Subtraction of Rational Expressionsvii431Mid-Chapter Test: Sections 7.1–7.4 4397.57.67.77.8Complex Fractions 439Solving Rational Equations 445Rational Equations: Applications and Problem SolvingVariation 463Chapter 7 Summary 473Chapter 7 Review Exercises 476Chapter 7 Practice Test 478Cumulative Review Test 4798Functions and Their Graphs 4534818.1 More on Graphs 4828.2 Functions 4908.3 Linear Functions 509Mid-Chapter Test: Sections 8.1–8.3 5168.4 Slope, Modeling, and Linear Relationships8.5 The Algebra of Functions 534Chapter 8 Summary 544Chapter 8 Review Exercises 547Chapter 8 Practice Test 550Cumulative Review Test 5519Systems of Linear Equations temsSystemsSystemsofofofof516553Equations Graphically 554Equations by Substitution 562Equations by the Addition Method 569Linear Equations in Three Variables 577Mid-Chapter Test: Sections 9.1–9.4 5859.5 Systems of Linear Equations: Applications and Problem Solving 5859.6 Solving Systems of Equations Using Matrices 5999.7 Solving Systems of Equations Using Determinants and Cramer’s Rule 608Chapter 9 Summary 615Chapter 9 Review Exercises 620Chapter 9 Practice Test 623Cumulative Review Test 62410 Inequalities in One and Two Variables 62610.1 Solving Linear Inequalities in One Variable 62710.2 Solving Equations and Inequalities ContainingAbsolute Values 642Mid-Chapter Test: Sections 10.1–10.2 65210.3 Graphing Linear Inequalities in Two Variables and Systemsof Linear Inequalities 652Chapter 10 Summary 663Chapter 10 Review Exercises 665Chapter 10 Practice Test 666Cumulative Review Test 667A01 RUND5089 05 AIE FM.indd 71/6/18 8:06 PM
viiiContentsSample Preface. Not for Distribution.11 Roots, Radicals, and Complex Numbers 11.111.211.311.4Roots and RadicalsRational ExponentsSimplifying RadicalsAdding, Subtracting,669677686and Multiplying Radicals668693Mid-Chapter Test: Sections 11.1–11.4 70111.5 Dividing Radicals 70111.6 Solving Radical Equations 71111.7 Complex Numbers 723Chapter 11 Summary 731Chapter 11 Review Exercises 735Chapter 11 Practice Test 738Cumulative Review Test 73912 Quadratic Functions 74012.1 Solving Quadratic Equations by Completing the Square 74112.2 Solving Quadratic Equations by the Quadratic Formula 75112.3 Quadratic Equations: Applications and Problem Solving 764Mid-Chapter Test: Sections 12.1–12.3 77312.4 Equations Quadratic in Form 77412.5 Graphing Quadratic Functions 78312.6 Quadratic, Polynomial, and Rational Inequalities in One VariableChapter 12 Summary 816Chapter 12 Review Exercises 820Chapter 12 Practice Test 824Cumulative Review Test 82513 Exponential and Logarithmic Functions 13.113.213.313.4Composite and Inverse FunctionsExponential Functions 839Logarithmic Functions 848Properties of Logarithms 856805826827Mid-Chapter Test: Sections 13.1–13.4 86213.5 Common Logarithms 86313.6 Exponential and Logarithmic Equations 87013.7 Natural Exponential and Natural Logarithmic FunctionsChapter 13 Summary 888Chapter 13 Review Exercises 892Chapter 13 Practice Test 894Cumulative Review Test 89514 Conic Sections 14.1 The Parabola and the Circle14.2 The Ellipse 910876897898Mid-Chapter Test: Sections 14.1–14.2 91714.3 The HyperbolaA01 RUND5089 05 AIE FM.indd 89181/6/18 8:06 PM
ContentsSample Preface. Not for Distribution.14.4 Nonlinear Systems of Equations and Their ApplicationsChapter 14 Summary 934Chapter 14 Review Exercises 937Chapter 14 Practice Test 939Cumulative Review Test 940ix92615 Sequences, Series, and the Binomial Theorem 94115.1 Sequences and Series 94215.2 Arithmetic Sequences and Series 94915.3 Geometric Sequences and Series 958Mid-Chapter Test: Sections 15.1–15.3 97015.4 The Binomial Theorem 970Chapter 15 Summary 976Chapter 15 Review Exercises 979Chapter 15 Practice Test 982Cumulative Review Test 983AppendicesAppendix A Review of Decimals and Percent 984Appendix B Determining the Greatest Common Factor and Least CommonDenominator 988Appendix C Geometry 990Appendix D Review of Exponents, Polynomials, and Factoring 995Answers* A1Applications Index I1Subject Index I5Photo Credits P1*Additional instructor answers for Graphing Exercises can be found on page G1.A01 RUND5089 05 AIE FM.indd 91/6/18 8:06 PM
Sample Preface. Not for Distribution.A01 RUND5089 05 AIE FM.indd 101/6/18 8:06 PM
Sample Preface. Not for Distribution.PrefaceWelcome to the 5th edition of Elementary and IntermediateAlgebra for College Students! This book has been used bythousands of students and other adults who have neverbeen exposed to algebra or those who have been exposedbut need a refresher course. Our primary goal was to writea book that students can read, understand, and enjoy. Toachieve this goal we have used short sentences, clear explanations, and many detailed, worked-out examples. Wehave tried to make the book relevant to college students byusing practical applications of algebra throughout the text.New to This EditionOne 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 Fifth 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:Content Changes Many discussions throughout the text have beenthoroughly revised for readability and improvedexplanation of key concepts. Whenever possible, avisual example or diagram is used to explain concepts and procedures. 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 complexand include more direct matching of the bookexamples and the corresponding exercises inMyLab Math. This creates a better experiencethroughout for students as well as making thematerial in the book better connected to thehomework 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 Exercise references at the end of workedexamples recommend exercises that are closelymatched to the examples and provide studentswith a framework with which to work key exercises. These have been carefully written to bettermatch the worked examples.–– Warm-Up Exercises have been revised to better reflect key vocabulary words, concepts, andf ormulas needed to perform the remainder of theexercise set. 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. The pedagogical use of color has been enhancedand continues to support a more visual approach tolearning algebra. Interval notation is now introduced in Section 2.8. Additional material on fractions has been added tohelp students with concepts such as rational expressions. Material on functions has been revised for greaterclarity. Applications have been updated throughout thebook. The MyLab Math course itself includes extensiveenhancements to improve outcomes for students:–– The addition of Skill Builder exercises–– Author-developed Sample Assignments thatinstructors can assign to utilize all of the newexercise enhancements–– Learning Catalytics can be accessed from theMyLab Math course–– Fully accessible PowerPoint slidesFeatures of the TextAccuracyAccuracy 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.xiA01 RUND5089 05 AIE FM.indd 111/6/18 8:06 PM
xiiPrefaceSample Preface. Not for Distribution.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 explanation withinMyLab Math. By the time students complete the chapter,they should have the knowledge to work the problem.Goals of This ChapterThis feature on the chapter opener page gives studentsa preview of the chapter and also indicates where thismaterial 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.be very beneficial for your s tudents and should helpthem to achieve success in mathematics.Understanding AlgebraUnderstanding Algebra boxes appear in the marginthroughout the text. Placed at key points, UnderstandingAlgebra boxes help students focus on the important concepts and facts that they need to master.Helpful HintsThe Helpful Hint boxes offer useful suggestions for problem solving and other varied topics. They are set off ina special manner so that students will be sure to readthem.Keyed Section ObjectivesAvoiding Common ErrorsEach 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.Common student errors are illustrated. Explanationsof why the shown procedures are incorrect are given.Explanations of how students may avoid such errors arealso presented.Problem SolvingExercise SetsPólya’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 reinforcethe concepts as students work the exercises. Throughthese exercises, students have the opportunity to immediately apply what they have learned. After each example, Now Try Exercises are indicated in orange typesuch as Now Try Exercise 27 . They are also indicated ingreen type in 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 shouldA01 RUND5089 05 AIE FM.indd 12The exercise sets are broken into three main categories:Warm-Up Exercises, Practice the Skills, and ProblemSolving. Many exercise sets also contain Concept/Writing Exercises, Challenge Problems, and/or GroupActivities. Each exercise set is graded in difficulty,and the exercises are paired. The early problems helpdevelop the students’ confidence, and then studentsare eased gradually into the more difficult problems. Asufficient number and variety of examples are given ineach section for students to successfully complete eventhe more difficult exercises. The number of exercisesin each section is more than ample for student assignments and practice.Warm-Up ExercisesThe exercise sets begin with Warm-
3 Applications of Algebra 176 3.1 Changing Application Problems into Equations 177 3.2 Solving Application Problems 191 Mid-Chapter Test: Sections 3.1–3.2 202 3.3 Geometric Problems 203 3.4 Motion, Money, and Mixture Problems 210 v A01_RUND5089_05_AIE_FM.indd 5 1/6/18 8:06 PM Sample Preface. Not for Distribution.
Robert Gerver, Ph.D. North Shore High School 450 Glen Cove Avenue Glen Head, NY 11545 gerverr@northshoreschools.org Rob has been teaching at . Algebra 1 Financial Algebra Geometry Algebra 2 Algebra 1 Geometry Financial Algebra Algebra 2 Algebra 1 Geometry Algebra 2 Financial Algebra ! Concurrently with Geometry, Algebra 2, or Precalculus
Intermediate Algebra Course Descripon and Competencies for Intermediate Algebra 4418 C o u rs e D e s c r i p o n Intermediate Algebra is designed to strengthen the students’ conceptual and procedural algebraic skills by creang a bridge for skills from Algebra I and Geometr y to future mathemacal endeavours in a progression that will increase .
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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
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