Preview Algebra for College Students (9th Edition) by Margaret L. Lial, John Hornsby, Terry McGinnis (2019)

Preview Algebra for College Students (9th Edition) by Margaret L. Lial, John Hornsby, Terry McGinnis (2019) Preview Algebra for College Students (9th Edition) by Margaret L. Lial, John Hornsby, Terry McGinnis (2019) Preview Algebra for College Students (9th Edition) by Margaret L. Lial, John Hornsby, Terry McGinnis (2019) Preview Algebra for College Students (9th Edition) by Margaret L. Lial, John Hornsby, Terry McGinnis (2019)

A LG E B RA FO R CO LLE G E S T U D E NT S LIAL / HORNSBY / McGINNIS ninth edition Get the Most Out of MyLab Math When it comes to developmental math, we know one size does not fit all Pearson’s solutions offer market-leading content written by our author-educators, tightly integrated with the #1 choice in digital learning-MyLab Math MyLab Math is the teaching and learning platform that empowers instructors to reach every student By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student • Flexible Platform— Your course is unique Whether you’d like to build your own assignments, structure students’ work with a learning path, or set prerequisites, you have the flexibility to easily create your course to fit your needs • Personalized Learning—Each student learns at a different pace Personalized learn- ing pinpoints the areas each student needs to practice, giving every student the support they need—when and where they need it—to be successful A variety of options are available to personalize learning in MyLab Math: ❍❍ ❍❍ With Personalized Homework, students take a quiz or test and receive a subsequent homework assignment that is personalized based on their performance This way, students can focus on just the topics they have not yet mastered Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives Available for select MyLab™ courses Visit pearson.com/mylab/math and click Get Trained to make sure you’re getting the most out of MyLab Math EDITION Algebra for College Students Margaret L Lial American River College John Hornsby University of New Orleans Terry McGinnis Vice President, Courseware Portfolio Management: Chris Hoag Director, Courseware Portfolio Management: Michael Hirsch Courseware Portfolio Manager: Karen Montgomery Courseware Portfolio Assistant: Kayla Shearns Managing Producer: Scott Disanno Content Producer: Lauren Morse Producers: Stacey Miller and Noelle Saligumba Managing Producer: Vicki Dreyfus Associate Content Producer, TestGen: Rajinder Singh Content Managers, MathXL: Eric Gregg and Dominick Franck Manager, Courseware QA: Mary Durnwald Senior Product Marketing Manager: Alicia Frankel Product Marketing Assistant: Brooke Imbornone Senior Author Support/Technology Specialist: Joe Vetere Full Service Vendor, Cover Design, Composition: Pearson CSC Full Service Project Management: Pearson CSC (Carol Merrigan) Cover Image: Borchee/E+/Getty Images Copyright © 2020, 2016, 2012 by Pearson Education, Inc 221 River Street, Hoboken, NJ 07030 All Rights Reserved Printed in the United States of America This publication is protected by copyright, and permission should be obtained 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 appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/ NOTICE: This work is solely for the use of instructors and administrators for the purpose of teaching courses and assessing student learning Unauthorized dissemination, publication or sale of the work, in whole or in part (including posting on the internet) will destroy the integrity of the work and is strictly prohibited Acknowledgments of third-party content appear on page C-1, which constitutes an extension of this copyright page PEARSON, ALWAYS LEARNING, MyLab™ Math, MathXL, and TestGen are exclusive trademarks in the U.S and/or other countries owned by Pearson Education, Inc or its affiliates Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc or its affiliates, authors, licensees or distributors Library of Congress Cataloging-in-Publication Data Names: Lial, Margaret L., author | Hornsby, John, 1949- author | McGinnis,   Terry, author Title: Algebra for college students Description: 9th edition / Margaret L Lial (American River College), John   Hornsby (University of New Orleans), Terry McGinnis | Boston : Pearson,   [2020] | Includes index Identifiers: LCCN 2019000106 | ISBN 9780135160664 (student edition) | ISBN   0135160669 (student edition) Subjects: LCSH: Algebra Textbooks Classification: LCC QA154.3 L53 2020 | DDC 512.9 dc23 LC record available at https://lccn.loc.gov/2019000106 1 19 ISBN 13: 978-0-13-516066-4 ISBN 10: 0-13-516066-9 CONTENTS Preface vii Study Skills  S-1 STUDY SKILL 1  Using Your Math Text  S-1 STUDY SKILL 6  Managing Your Time  S-6 STUDY SKILL 2  Reading Your Math Text  S-2 STUDY SKILL 7  Reviewing a Chapter  S-7 STUDY SKILL 3  Taking Lecture Notes  S-3 STUDY SKILL 8  Taking Math Tests  S-8 STUDY SKILL 4  Completing Your Homework  S-4 STUDY SKILL 9  Analyzing Your Test Results  S-9 STUDY SKILL 5  Using Study Cards  S-5 STUDY SKILL 10 Preparing for Your Math Final Exam S-10 R Review of the Real Number System  R.1 Fractions, Decimals, and Percents  R.2 Basic Concepts from Algebra  14 R.3 Operations on Real Numbers  26 R.5 Properties of Real Numbers  45 Chapter R Summary  52 Chapter R Test  54 R.4 Exponents, Roots, and Order of Operations  36 Linear Equations, Inequalities, and Applications  55 1.1 Linear Equations in One Variable  56 1.7 Absolute Value Equations and Inequalities  125 1.2 Formulas and Percent  65 SUMMARY EXERCISES  Solving Linear and Absolute Value 1.3 Applications of Linear Equations  78 1.4 Further Applications of Linear Equations  92 SUMMARY EXERCISES  Applying Problem-Solving Techniques 101 1.5 Linear Inequalities in One Variable  103 1.6 Set Operations and Compound Inequalities  116 Equations and Inequalities  136 Chapter Summary  137 Chapter Review Exercises  142 Chapter Mixed Review Exercises  145 Chapter Test  146 Chapters R and Cumulative Review Exercises 148 Linear Equations, Graphs, and Functions  149 2.1 Linear Equations in Two Variables  150 2.5 Introduction to Relations and Functions  199 2.2 The Slope of a Line  161 2.6 Function Notation and Linear Functions  210 2.3 Writing Equations of Lines  176 SUMMARY EXERCISES  Finding Slopes and Equations of Lines  191 2.4 Linear Inequalities in Two Variables  192 Chapter Summary  219 Chapter Review Exercises  222 Chapter Mixed Review Exercises  224 Chapter Test  225 Chapters R–2 Cumulative Review Exercises  227 iii iv Contents Systems of Linear Equations  229 3.1 Systems of Linear Equations in Two Variables 230 3.2 Systems of Linear Equations in Three Variables 245 3.3 Applications of Systems of Linear Equations 254 Exponents, Polynomials, and Polynomial Functions  279 4.1 Integer Exponents  280 4.2 Scientific Notation  290 4.3 Adding and Subtracting Polynomials  296 4.4 Polynomial Functions, Graphs, and Composition 302 4.5 Multiplying Polynomials  315 4.6 Dividing Polynomials  324 Chapter Summary  331 Chapter Review Exercises  334 Chapter Mixed Review Exercises  337 Chapter Test  337 Chapters R–4 Cumulative Review Exercises 338 Factoring 341 5.1 Greatest Common Factors and Factoring by Grouping  z - 26 - k = - 1k -1 - 26 r = 1r 3x 8 x = = 1x x = x 5p and -21p -6x2 and 9x2 Like terms 3m and 16x 7y and -3y Unlike terms Different variables Different exponents on the same variable OBJECTIVE 4  Use the commutative and associative properties Simplifying expressions as in Examples 2(a) and (b) is called combining like terms Only like terms may be combined To combine like terms in an expression such as -2m + 5m + - 6m + 8, we need two more properties From arithmetic, we know that the following are true + = 12 + = 12 and # = 27 # = 27 and The order of the numbers being added or multiplied does not matter The same answers result The following computations are also true 15 + 72 + = 12 + = 14 + 17 + 22 = + = 14 15 # 72 # = 35 # = 70 # 17 # 22 = # 14 = 70 The grouping of the numbers being added or multiplied does not matter The same answers result These arithmetic examples can be extended to algebra Commutative and Associative Properties For any real numbers a, b, and c, the following hold true a+b=b+a ab = ba   Commutative properties (The order of the two terms or factors changes.) Examples:  + 1-32 = -3 + 9, 91 -32 = 1-329 a + b + c2 = a + b + c a bc2 = ab c (1)1* Numerical Coefficient Term The inverse properties “undo” addition or multiplication Putting on your shoes when you get up in the morning and then taking them off before you go to bed at night are inverse operations that undo each other Expressions such as 12m and 5n from Example are examples of terms A term is a number or the product of a number and one or more variables raised to powers The numerical factor in a term is the numerical coefficient, or just the coefficient Terms with exactly the same variables raised to exactly the same powers are like terms Otherwise, they are unlike terms (1)1* ▼▼ Terms and Their Coefficients Associative properties   (The grouping among the three terms or factors changes, but the order stays the same.) Examples:  + 18 + 92 = 17 + 82 + 9, # 18 # 92 = 17 # 82 # SECTION R.5   Properties of Real Numbers 49 The commutative properties are used to change the order of the terms or factors in an expression Think of commuting from home to work and then from work to home The associative properties are used to regroup the terms or factors of an expression Think of associating the grouped terms or factors NOW TRY EXERCISE Simplify -7x + 10 - 3x - + x EXAMPLE Using the Commutative and Associative Properties Simplify -2m + 5m + - 6m + = 1-2m + 5m2 + - 6m + Associative property = 3m + - 6m + Add inside parentheses = 1-2 + 52m + - 6m + Distributive property The next step would be to add 3m and 3, but they are unlike terms To combine 3m and -6m, we use the associative and commutative properties, inserting parentheses and brackets according to the rules for order of operations = 33m + 13 - 6m24 + Associative property = 313m + -6m42 + 34 + Associative property = -3m + 13 + 82 Associative property = 33m + 1-6m + 324 + Commutative property = 1-3m + 32 + Combine like terms = -3m + 11 Add In practice, many of these steps are not written down, but it is important to realize that the commutative and associative properties are used whenever the terms in an expression are rearranged and regrouped to combine like terms NOW TRY EXAMPLE Using the Properties of Real Numbers Simplify each expression (a) 5y - 8y - 6y + 11y = 15 - - + 112y = 2y (b) 3x + - 51x + 12 - Combine like terms Be careful with signs = 3x + - 5x - - Distributive property = 3x - 5x + - - Commutative property = -2x - Combine like terms (c) - 13m + 22 NOW TRY ANSWER -9x + Distributive property = - 113m + 22 Identity property = - 3m - Distributive property = - 3m Combine like terms 50 CHAPTER R    Review of the Real Number System NOW TRY EXERCISE (d) 3x1521y2 Simplify each expression (a) -31t - 42 - t + 15 (b) 7x - 14x - 22 (c) 5x16y2 (d) 315x - 72 - 81x + 42 = 33x1524y Order of operations = 3315x24y Commutative property = 115x2y Multiply = 331x # 524y = 313 # 52x4y = 151xy2 Associative property Associative property Associative property = 15xy As previously mentioned, many of these steps are not usually written out (e) 413x - 52 - 214x + 72 = 12x - 20 - 8x - 14 Distributive property = 12x - 8x - 20 - 14 Commutative property = 4x - 34 Combine like terms Like terms may be combined by adding or subtracting the coefficients of the terms and keeping the same variable factors NOW TRY NOW TRY ANSWERS (a)  -4t + 27  (b)  3x + (c)  30xy  (d)  7x - 53 R.5 Exercises Video solutions for select problems available in MyLab Math ! CAUTION Be careful The distributive property does not apply in Example 4(d) because there is no addition or subtraction involved 13x21521y2 ≠ 13x2152 # 13x21y2 FOR EXTRA HELP MyLab Math Concept Check  Choose the correct response The identity element for addition is A.  -a  B.  0  C.  1  D.  a The additive inverse of a is A.  -a  B.  0  C.  1  D.  a The identity element for multiplication is A.  -a  B.  0  C.  1  D.  a The multiplicative inverse of a, where a ≠ 0, is A.  -a  B.  0  C.  1  D.  a Concept Check  Complete each statement The distributive property provides a way to rewrite a product such as a1b + c2 as the sum _  The commutative property is used to change the _ of two terms or factors The associative property is used to change the _ of three terms or factors Like terms are terms with the _ variables raised to the _ powers When simplifying an expression, only _ terms can be combined 10 The numerical coefficient in the term -7yz is _  SECTION R.5   Properties of Real Numbers 51 Simplify each expression See Examples and 11 21m + p2 12 31a + b2 13 -121x - y2 14 -101p - q2 15 5k + 3k 16 6a + 5a 17 7r - 9r 18 4n - 6n 19 -8z + 4w 20 -12k + 3r 21 a + 7a 22 s + 9s 23 x + x 24 a + a 26 -13m - n2 27 -1 -x - y2 28 -1-3x - 4y2 25 -12d - f 29 21x - 3y + 2z2 30 813x + y - 5z2 Simplify each expression See Examples 1– 4 31 -12y + 4y + 3y + 2y 32 -5r - 9r + 8r - 5r 33 -6p + - 4p + + 11p 34 -8x - 12 + 3x - 5x + 35 31k + 22 - 5k + + 36 51r - 32 + 6r - 2r + 37 10 - 14y + 82 39 10x1321y2 38 - 19y + 52 40 8x1621y2 41 - 112w217z2 42 - 118w215z2 43 31m - 42 - 21m + 12 44 61a - 52 - 41a + 62 45 0.2518 + 4p2 - 0.516 + 2p2 46 0.4110 - 5x2 - 0.815 + 10x2 47 -12p + 52 + 312p + 42 - 2p 48 -17m - 122 + 214m + 72 - 6m 49 + 312z - 52 - 314z + 62 - 50 -4 + 414k - 32 - 612k + 82 + Complete each statement so that the indicated property is illustrated Simplify each answer if possible See Examples 1– 4 51 5x + 8x = 52 9y - 6y = (distributive property) 53 519r2 = (associative property) 55 5x + 9y = 57 # = (distributive property) 54 -4 + 112 + 82 = (associative property) 56 -5 # = (commutative property) (commutative property) 58 -12x + = (identity property) 1 59 - ty + ty = 4 (identity property) 60 - (inverse property) 61 81 -4 + x2 = (distributive property) 63 010.875x + 9y2 = a- b = (inverse property) 62 31x - y + z2 = (distributive property) 64 010.35t + 12u2 = (multiplication property of 0) (multiplication property of 0) 65 Concept Check  Give an “everyday” example of a commutative operation 66 Concept Check  Give an “everyday” example of inverse operations 52 CHAPTER R    Review of the Real Number System The distributive property can be used to mentally perform calculations 38 # 17 + 38 # = 38117 + 32 Distributive property = 381202 Add inside the parentheses = 760 Multiply Use the distributive property to calculate each value mentally 67 96 # 19 + # 19 8 70 1172 + 1132 5 # # 68 27 # 60 + 27 # 40 69 58 71 8.751152 - 8.75152 72 4.311692 + 4.311312 -8 RELATING CONCEPTS For Individual or Group Work  (Exercises 73 –78) When simplifying an expression, we usually some steps mentally Work Exer­ cises 73–78 in order, providing the property that justifies each statement in the given simplification (These steps could be done in other orders.) 3x + + 2x + 73 74 75 76 77 78 Chapter R = 13x + 42 + 12x + 72 _ = 3x + 14 + 2x2 + 7   _ = 3x + 12x + 42 + 7   _ = 13x + 2x2 + 14 + 72 _ = 13 + 22x + 14 + 72   _ = 5x + 11   _ Summary Key Terms R.1 fractions numerator denominator proper fraction improper fraction lowest terms mixed number reciprocals decimal terminating decimal repeating decimal percent R.2 set elements (members) finite set natural (counting) numbers infinite set whole numbers empty (null) set variable number line integers coordinate graph rational numbers irrational numbers real numbers additive inverse (opposite, negative) signed numbers absolute value equation inequality R.3 sum difference product quotient reciprocal (multiplicative inverse) dividend divisor R.4 factors exponent (power) base exponential expression square root positive (principal) square root negative square root constant algebraic expression R.5 identity element for addition (additive identity) identity element for multiplication (multiplicative identity) term coefficient (numerical coefficient) like terms unlike terms ... Names: Lial, Margaret L., author | Hornsby, John, 1949- author | McGinnis,   Terry, author Title: Algebra for college students Description: 9th edition / Margaret L Lial (American River College) , John. .. Available for select MyLab™ courses Visit pearson.com/mylab/math and click Get Trained to make sure you’re getting the most out of MyLab Math EDITION Algebra for College Students Margaret L.. . system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise For information regarding permissions, request forms, and the appropriate contacts