Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Photo Credits Cover Thinkstock/Alamy; iv (tl bl br) File Photo, (tc tr) The McGraw-Hill Companies, (cl c) Doug Martin, (cr) Aaron Haupt; v (1 11 12) The McGraw-Hill Companies; v (5 10 13 14) File Photo; ix Digital Vision/PunchStock; vii Ian Grant/Alamy; viii Medioimages/PunchStock; x CORBIS; 2–3 Ray Kachatorian/Getty Images; 17 Martin Harvey/Peter Arnold, Inc.; 40–41 John Giustina/Getty Images; 78–79 Stockbyte/Getty Images; 80 Stockdisc/Getty Images; 85 cre8ive studios/iStock; 91 GABRIEL BOUYS/AFP/Getty Images; 92 Michael Newman/PhotoEdit; 99 James Leynse/Corbis Copyright © 2008 by The McGraw-Hill Companies, Inc All rights reserved Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-878210 MHID: 0-07-878210-4 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 4B California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Volume Ratios, Rates, and Percents 3A Chapter Ratios and Rates 3A Chapter Percents, Fractions, and Decimals 3B Chapter Using Percents 3B Chapter Rates and Proportional Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume Functions and Equations 5A Chapter Patterns and Relationships 5A Chapter Graphing 5B Chapter Proportional Relationships 5B Chapter The Relationship Between Graphs and Functions Volume Measurement 6A Chapter How Measurements Are Made 6A Chapter Length and Area in the Real World 6B Chapter Exact Measures in Geometry 6B Chapter Angles and Circles iii Authors and Consultants AUTHORS Frances Basich Whitney Kathleen M Brown Dixie Dawson Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Math Curriculum Leader Long Beach Unified Long Beach, California Philip Gonsalves Robyn Silbey Kathy Vielhaber Mathematics Coordinator Alameda County Office of Education Hayward, California Math Specialist Montgomery County Public Schools Gaithersburg, Maryland Mathematics Consultant St Louis, Missouri Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Dinah Zike Educational Consultant, Dinah-Might Activities, Inc San Antonio, Texas CONSULTANTS Assessment Donna M Kopenski, Ed.D Math Coordinator K–5 City Heights Educational Collaborative San Diego, California iv Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc CONTRIBUTING AUTHORS California Advisory Board CALIFORNIA ADVISORY BOARD Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program They reviewed the table of contents, the prototype of the Student Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan Linda Anderson Cheryl L Avalos Bonnie Awes Kathleen M Brown 4th/5th Grade Teacher Oliveira Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Carol Cronk Audrey M Day Jill Fetters Grant A Fraser, Ph.D Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Classroom Teacher Rosa Parks Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel Donna M Kopenski, Ed.D Michael A Pease Chuck Podhorsky, Ph.D Mathematics Department Chair Frontier High School Bakersfield, California Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Math Coach Aspire Public Schools Oakland, California Math Director City Heights Educational Collaborative San Diego, California Arthur K Wayman, Ph.D Frances Basich Whitney Mario Borrayo Melissa Bray Professor Emeritus California State University, Long Beach Long Beach, California Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA Teacher Rosa Parks Elementary San Diego, California K–8 Math Resource Teacher Modesto City Schools Modesto, California v California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction Melody McGuire Math Teacher California College Preparatory Academy Oakland, California 6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California Eppie Leamy Chung Monica S Patterson Teacher Modesto City Schools Modesto, California Educator Aspire Public Schools Modesto, California Judy Descoteaux Rechelle Pearlman Mathematics Teacher Thornton Junior High School Fremont, California 4th Grade Teacher Wanda Hirsch Elementary School Tracy, California Paul J Fogarty Armida Picon Mathematics Lead Aspire Public Schools Modesto, California 5th Grade Teacher Mineral King School Visalia, California Lisa Majarian Anthony J Solina Classroom Teacher Cottonwood Creek Elementary Visalia, California Lead Educator Aspire Public Schools Stockton, California vi Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Bobbi Anne Barnowsky Volume 4A The Core Processes of Mathematics Chapter Operations and Equality 1-1 Addition and Subtraction Operations 3AF1.0 1-2 Multiplication and Division Operations .11 3AF1.0 Progress Check .18 1-3 Equality 19 4AF2.1, 4AF2.2 1-4 Operations with Unknown Quantities 25 4AF1.1 Progress Check .31 Assessment Chapters and are contained in Volume 4A Chapters 3, 4, and are contained in Volume 4B Standards Addressed in This Chapter 3AF1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable) 4AF2.1 Know and understand that equals added to equals are equal 4AF2.2 Know and understand that equals multiplied by equals are equal Study Guide .32 Chapter Test .36 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Standards Practice 38 Point Lobos State Park vii Contents Chapter Math Fundamentals Standards Addressed in This Chapter 2-1 Commutative Property 42 2AF1.1, 3AF1.5 2-2 Associative Property .49 2AF1.1, 3AF1.5 Progress Check .56 2-3 Distributive Property 57 5AF1.3 2-4 Order of Operations 63 7AF1.2 Progress Check .69 2AF1.1 Use the commutative and associative rules to simplify mental calculations and to check results 3AF1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if × = 35, then what is × 5? and if × × = 105, then what is × × 5?) 5AF1.3 Know and use the distributive property in equations and expressions with variables 7AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2 Assessment Study Guide .70 Chapter Test .74 Standards Practice 76 Mustard plants in Napa Valley Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc viii Contents Chapter Math Expressions 3-1 Algebraic Expressions .4 7AF1.1 3-2 Translating Verbal Phrases into Mathematical Symbols 11 5AF1.2, 7AF1.1 Progress Check .20 3-3 Simplify Expressions 21 7AF1.3 3-4 Evaluate Variable Expressions 29 5AF1.2, 6AF1.2, 7AF1.3 Progress Check .35 Assessment Study Guide .36 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Chapter Test .40 Chapters and are contained in Volume 4A Chapters 3, 4, and are contained in Volume 4B Standards Addressed in This Chapter 5AF1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution 6AF1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables 7AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A) 7AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used Standards Practice 42 Burney Falls ix Contents Chapter Linear Equations Standards Addressed in This Chapter 4-1 Translate Word Phrases into Equations .46 7AF1.1 4-2 Solve Equations Using Addition and Subtraction .53 4AF2.1, 7AF4.0 Progress Check 60 4-3 Solve Equations Using Multiplication and Division 61 4AF2.2, 7AF4.0 4-4 Multi-Step Equations 67 7AF4.0 Progress Check 74 4-5 Symbolic Computation 75 4AF2.1 Know and understand that equals added to equals are equal 4AF2.2 Know and understand that equals multiplied by equals are equal 7NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications 7AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A) 7AF4.0 Students solve simple linear equations and inequalities over the rational numbers 7NS1.3 Assessment Chapter Test 86 Standards Practice 88 x Alabama Hills, Owens Valley Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Study Guide 82 Step by Step Practice 5 + x ≤ 65 Step Locate the side of the inequality with the variable What addition operation is used? Step What is the inverse operation? + x ≤ 65 x ≤ 62.5 subtraction Solve each inequality k - < 12 addition inverse operation: Add to each side k < 21 Copyright © by The McGraw-Hill Companies, Inc m + > 13 inverse operation: Subtract subtraction from each side m>7 + p ≤ 1.9 p ≤ -5.1 w - 0.8 ≥ w ≥ 3.8 GO ON Lesson 5-2 Solve Inequalities Using Addition and Subtraction 101 Step by Step Problem-Solving Practice Problem-Solving Strategies Solve 10 HEALTH A person should eat no more than 2,400 milligrams of sodium per day Carlos’s breakfast contained 660 milligrams of sodium His lunch contained 1,300 milligrams of sodium What is the most sodium, s, Carlos should eat at dinner? Understand Draw a diagram Look for a pattern Guess and check Solve a simpler problem ✓ Work backward Read the problem Write what you know Carlos should have at most 2,400 milligrams of sodium each day Carlos has already had 660 and 1,300 milligrams today Plan Pick a strategy One strategy is to work backward Start with the total sodium for the day Subtract what Carlos has already had Use that number to write an inequality Solve 2,400 total sodium - 1,740 660 breakfast - subtotal 1,300 lunch = 1,740 = subtotal = = 440 dinner the most Write the inequality s ≤ 440 Carlos should eat 440 milligrams of sodium or less at dinner Check Add the milligrams of sodium that Carlos had for breakfast (660), lunch (1,300), and dinner (s) Substitute your answer for s to check 660 + 1,300 + 440 ≤ 2,400 2,400 ≤ 2,400 102 Chapter Inequalities Copyright © by The McGraw-Hill Companies, Inc Is the last number the most or the least sodium that Carlos should have at dinner? 11 MUSIC A CD holds up to 80 minutes of music Raven is making a CD She has 53 minutes of music on a play list Write and solve an inequality to find m, the number of minutes of music Raven can add to the CD Check off each step 53 + m ≤ 80; m ≤ 27 12 ✔ Understand ✔ Plan ✔ Solve ✔ Check AIRPLANES The ATR-42 can hold a maximum of 66 passengers There are 22 passengers on board Write and solve an inequality to find n, the number of additional passengers that can board the plane n + 22 ≤ 66; n ≤ 44 AIRPLANES The ATR-42 is a turboprop plane Is 44 a solution of the inequality r - 31 < 15? Explain 13 Yes; substitute 44 for r and then solve: 44 - 31 < 15; 13 < 15 Copyright © by The McGraw-Hill Companies, Inc Skills, Concepts, and Problem Solving Solve each inequality 14 + t > 56 t> 16 18 50 + g ≥ 3.1 g≥ 15 k> 17 0.1 h + ≤ 19 19 94 < f + _ 93 < f 10 b - 4.2 ≤ 1.2 b≤ h ≤ 18 20 10 + k > 20 5.4 y - ≥ 54 y ≥ 62 21 2.8 > a - 1.8 4.6 > a GO ON Lesson 5-2 Solve Inequalities Using Addition and Subtraction Gabriel Bouys/AFP/Getty Images 103 22 j - 21 < 19 40 j< 24 26 + n > 23 n>2 y - ≤ 41.6 b> 25 d-1>0 27 29 31 3.8 + m ≥ 11.4 33 m ≥ 7.6 _ w≤ c - ≥ 36.9 f - > -2 2 32 32 f>0 3>4 x + _ + w ≤ c ≥ 40.9 d>1 30 17 y ≤ 46.6 28 b - > 12 9.2 + k < 21.6 k < 12.4 Copyright © by The McGraw-Hill Companies, Inc Solve 34 ENTERTAINMENT Kristen wants to buy tickets to the circus for her family and friends There are 14 people who are going to the circus Write and solve an inequality to find n, the number of additional people needed so that Kristen can get the lower price for groups 14 + n ≥ 20; n ≥ 35 NUMBER SENSE The sum of Jessica’s age, x, and Benito’s age, 12, is at least 25 Write and solve an inequality to find Jessica’s age x + 12 ≥ 25; x ≥ 13 104 Chapter Inequalities Michael Newman/PhotoEdit ENTERTAINMENT The circus offers reduced prices for groups of 20 or more people Vocabulary Check Write the vocabulary word that completes each sentence 36 37 38 39 A number sentence that compares two unequal expressions and uses < (is less than), > (is greater than), ≤ (is less than or equal to), ≥ (is greater than or equal to), or ≠ (is not equal to) to compare inequality two unequal expressions is called a(n) Addition The Property of Inequality states that adding the same amount to both sides of an inequality keeps the inequality balanced Addition and subtraction are inverse operations because they undo each other Writing in Math Explain how to solve the inequality 16 + v ≤ 17 Add -16 to each side of the inequality: 16 + (-16) + v ≤ 17 + (-16); v ≤ Spiral Review Solve Copyright © by The McGraw-Hill Companies, Inc 40 (Lesson 5-1, p 90) BAKING Mrs Diaz baked 60 cookies for a bake sale Sebastian ate some cookies There were less than 50 cookies left for the bake sale Write an inequality to find c, the number of cookies Sebastian ate 60 - c < 50 Solve each equation 41 22 + h = 31 h= 43 (Lesson 4-2, p 53) 42 Show that adding on each side of (19 + 5) = (16 + 8) results in a true equation (Lesson 1-3, p 19) a - 56 = 16 a= 44 72 Show that multiplying by on each side of (4 · 8) = (16 · 2) results in a true equation (Lesson 1-3, p 19) 24 + = 24 + 32 · = 32 · 31 = 31 96 = 96 Lesson 5-2 Solve Inequalities Using Addition and Subtraction 105 Chapter Progress Check (Lessons 5-1 and 5-2) Write the symbol that should be used for each inequality 7AF1.1 A number is greater than or equal to ≥ Nine divided by a number is less than 27 < Write the operation that should be used to solve each inequality 7AF1.1 g + ≤ 51 m - > 23 subtraction addition Translate each sentence to an inequality 7AF1.1 The product of twelve and a number is greater than thirty-eight The quotient of a number and four plus seven is less than or equal to sixty-four _ n ÷ + ≤ 64 or n +7 ≤ 64 12 · n > 38 or 12n > 38 Solve each inequality 7AF4.0 14 + a ≥ 53 39 n - < 110 n < 115 x - 36 < 41 x< 10 77 Copyright © by The McGraw-Hill Companies, Inc a≥ y + 26 ≤ 44 y≤ 18 Solve 7AF1.1, 7AF4.0 11 TRAVEL A train traveled 384 miles in less than hours Write an inequality and solve for s, the speed of the train 6s < 384; s < 64 106 Chapter Inequalities X XY Y Xµ OOK 12 ATH5 5EST H AT Y TEB /O K OO TEB 90 + 78 + 86 + x ≥ 332; x ≥ 78 ATH5EST X X X X X EST /O GRADES A student in Mr Kelso’s math class needs at least 332 points to earn a B Angelo’s scores on the first three tests are shown Write and solve an inequality to find x, the number of points Angelo needs to score on the fourth test to earn a B for the class Lesson 5-3 Solve Inequalities Using Multiplication and Division 7AF4.0 Students solve simple linear equations and inequalities over the rational numbers KEY Concept To solve inequalities with multiplication and division, you may need to change the inequality symbol Multiply or Divide by a Negative Number: inequality symbol does reverse Multiply or Divide by a Positive Number: inequality symbol does not reverse a and b are any a and b are any number number c is a positive number c is a negative number Multiplication Property of Inequality Copyright © by The McGraw-Hill Companies, Inc Division Property of Inequality If a < b, then a · c < b · c If a < b, then a · c > b · c If a > b, then a · c > b · c If a > b, then a · c < b · c _ _ _ _ _ _ a b If a < b, then c < c a b If a > b, then c > c a b If a < b, then c > c a b If a > b, then c < c These properties also hold true for a ≥ b and a ≤ b VOCABULARY Multiplication Property of Inequality When multiplying each side of an inequality by the same positive number, the inequality remains true When multiplying each side of an inequality by the same negative number, the inequality symbol reverses and the inequality remains true Division Property of Inequality When dividing each side of an inequality by the same positive number, the inequality remains true When dividing each side of an inequality by the same negative number, the inequality symbol reverses and the inequality remains true Example YOUR TURN! Solve 7z ≤ 63 Solve 8y ≥ 32 Locate the side of the inequality with the variable What operation is used? multiplication 7z ≤ 63 Locate the side of the inequality with the variable What operation is used? multiplication What is the inverse operation? division 7z _ _ ≤ 63 7 z≤9 Are you dividing by a positive or negative number? positive Will the symbol reverse? no What is the inverse operation? division Are you dividing by a positive or negative number? positive 8y ≥ 32 8y 32 ≥ Will the symbol reverse? no y≥ GO ON Lesson 5-3 Solve Inequalities Using Multiplication and Division 107 Example Solve _y > 5.1 Locate the side of the inequality with the variable What operation is used? division What is the inverse operation? multiplication y > 5.1 y · > 5.1 · 3 y > 15.3 _ YOUR TURN! Solve _ Locate the side of the inequality with the variable What operation is used? division What is the inverse operation? multiplication _ Example _p ≥ 2.1 _p _p ≥ 2.1 × ≥ 2.1 × 5 p ≥ 10.5 YOUR TURN! Solve - z ≤ 12 Solve -5z ≤ 40 Locate the side of the inequality with the variable What operation is used? division Locate the side of the inequality with the variable What operation is used? Are you dividing by a positive or negative number? negative Will the symbol reverse? yes - z ≤ 12 z - (-6) ≥ 12(-6) _ _ z ≥ -72 What is the inverse operation? division Are you dividing by a positive or negative negative number? Will the symbol reverse? yes -5z ≤ 40 -5z ≥ 40 _ _ –5 –5 z ≥ -8 108 Chapter Inequalities Copyright © by The McGraw-Hill Companies, Inc What is the inverse operation? multiplication multiplication Who is Correct? Solve 5d ≤ 60 Ying Kaylee Cesar 5d ≤ 60 5d ≤ 60 60 60 d≤1 5d ≤ 60 5d · ≤ 60 · d ≤ 300 5d ≤ 60 5d ≤ 60 5 12 d≤ _ _ _ _ Circle correct answer(s) Cross out incorrect answer(s) Guided Practice Write the operation that should be used to solve each inequality Will the symbol reverse? p division, yes multiplication, no -9k < 72 > 20 m division, no multiplication, yes 4b ≤ _ - ≥ Copyright © by The McGraw-Hill Companies, Inc Step by Step Practice n ≤ Solve - Step Locate the side of the inequality with the variable What division operation is used? Step What is the inverse operation? multiplication Step Are you multiplying by a positive or negative number? negative n - · -6 ≥2· -6 n ≥ -12 Step Will the symbol reverse? yes GO ON Lesson 5-3 Solve Inequalities Using Multiplication and Division 109 Solve each inequality -7c > 21 division -7 inverse operation: Divide each side by c< q ≥6 -0.3m < 36 m > -120 inverse operation: multiplication Multiply each side by q ≥ 48 0.6h < 54 h < 90 x≥ Step by Step Problem-Solving Practice Look for a pattern Guess and check Act it out ✓ Write an inequality Work backward SCHOOL Mrs Cheeti spent at least 270 minutes grading papers for 90 students Write and solve an inequality to find how long on average Mrs Cheeti spent grading each paper Understand -45 _ Problem-Solving Strategies Solve 11 x ≤ - 10 Read the problem Write what you know Mrs Cheeti spent at least 270 minutes grading papers Mrs Cheeti had 90 papers to grade Pick a strategy One strategy is to write an inequality Solve Let n = the number of minutes per paper Write an inequality that matches the situation n ≥ 90 270 _· number of minutes · number of papers ≥ total number of minutes Use the inverse operation to solve n · 90 ≥ 270 90n 270 ≥ 90 90 n≥ Mrs Cheeti spent at least Check Substitute than 3 90 ( Chapter Inequalities minutes grading each paper or any number greater for n to check ) ≥ 270 270 ≥ 270 110 3 Copyright © by The McGraw-Hill Companies, Inc Plan 12 MONEY Nadia bought 10 energy bars She gave the cashier a $20 bill and got change back Write and solve an inequality to find c, the cost of one energy bar Check off each step 10c < 20; c < 13 ✔ Understand ✔ Plan ✔ Solve ✔ Check BASEBALL Ginger accidentally broke a window with a baseball A new window costs at least $128 Write and solve an inequality to find x, the minimum amount Ginger should pay each month for the window to be paid off in months 8x ≥ 128; x ≥ 16 Is y > the solution of the inequality -4y > -12? Explain 14 No; when you divide by a negative, the inequalilty symbol must be reversed Copyright © by The McGraw-Hill Companies, Inc Skills, Concepts, and Problem Solving Solve each inequality b 15 _ ≤ 5x 12 16 15w > 7.5 60 ≤ 18 x < 14 - _ 13 -6d < 7.2 19 14p > 28 11m < 154 m < 14 s ≤ -50 20 r ≤9 _ 11 p>2 22 a ≥4 - _ 20 d > -1.2 24 -2s ≥ 100 w > 0.5 x > -182 21 17 r ≤ 99 23 a ≤ -80 25 x ≤ 12 x ≤ 48 17 b ≤ -85 26 -b ≥ _ -9c > 72 c < -8 GO ON Lesson 5-3 Solve Inequalities Using Multiplication and Division 111 Solve 27 ENTERTAINMENT The total cost of Susan’s purchase was at least $135 Write and solve an inequality to find x, the number of CDs Susan bought 15x ≥ 135; x ≥ 28 TEMPERATURE Mr Ramirez gave each of his 18 students at least colored pencils Write and solve an inequality to find n, the number of colored pencils Mr Ramirez gave out _n ≥ 5; n ≥ 90 18 ENTERTAINMENT Susan Vocabulary Check Write the vocabulary word that completes each sentence 29 bought some CDs for $15 each Multiplication The Property of Inequality states that multiplying each side of an inequality by the same positive number keeps the inequality true 30 division Multiplication and operations because they undo each other 31 z ≥ 13 Writing in Math Explain how to solve the inequality - are inverse Multiply each side of the inequality by -4 and reverse the symbol since -4 is a negative; z · -4 ≤ 13 · -4; z ≤ -52 _ Solve 32 (Lesson 5-2, p 97) HOBBIES A metro bus can hold a maximum of 90 passengers There are 53 passengers on the bus Write and solve an inequality to find n, the number of additional passengers the bus can hold n + 53 ≤ 90; n ≤ 37 Solve each equation 33 (Lesson 4-4, p 67) 4b + = 27 b= Name the like terms in each expression 35 5t - + 6t + 10 5t and 6t; -8 and 10 112 34 Chapter Inequalities IT Stock Free/SuperStock y -9=2 y= 66 (Lesson 3-3, p 21) 36 - c + + 7c -c and 7c; and Copyright © by The McGraw-Hill Companies, Inc Spiral Review Lesson 5-4 Solve Multi-Step Inequalities KEY Concept As with multi-step equations, you need to get the variable alone on one side of the inequality sign to solve multi-step linear inequalities To this, you use inverse operations more than one time First undo the addition or subtraction, using the Addition Property of Inequality Then undo the multiplication or division to get the variable alone using the Multiplication Property of Inequality 7AF4.0 Students solve simple linear equations and inequalities over the rational numbers 7NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications inverse operations operations that undo each other (Lesson 1-4, p 25) Addition Property of Inequality Adding the same amount to each side of an inequality keeps the inequality true (Lesson 5-2, p 97) 6TFBOJOWFSTFPQFSBUJPOmSTUUPJTPMBUF UIFUFSNXJUIUIFWBSJBCMF5IFPQQPTJUF PGJT ... thank the following professionals for their invaluable feedback during the development of the program They reviewed the table of contents, the prototype of the Student Study Guide, the prototype of. .. Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume. .. is the variable? The variable is the letter What is the constant? The constant is the number x -5 What is the coefficient? The coefficient is the number multiplied by the variable It is the