INSTRUCTOR’S
M
SOLUTIONS MANUAL
PR
DIACRITECH
E LEMENTARY A LGEBRA :
ES
G RAPHS AND A UTHENTIC
A PPLICATIONS
SI
THIRD EDITION
VE
G
Jay Lehmann
College of San Mateo
R
AD
ES
,M
PR
ES
SI
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher
make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this
VE
book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with,
or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2019, 2015, 2011 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
G
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
R
publisher. Printed in the United States of America.
AD
ES
ISBN-13: 978-0-13-479533-1
ISBN-10: 0-13-479533-4
, Contents
Chapter 1 Introduction to Modeling
M
1.1 Variables and Constants 1
1.2 Scatterplots 3
1.3 Exact Linear Relationships 5
PR
1.4 Approximate Linear Relationships 8
Chapter 1 Review Exercises 12
Chapter 1 Test 15
Chapter 2 Operations and Expressions
ES
2.1 Expressions 17
2.2 Operations with Fractions 18
2.3 Absolute Value and Adding Real Numbers 21
2.4 Change in a Quantity and Subtracting Real Numbers 24
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers 27
2.6 Exponents and Order of Operations 30
Chapter 2 Review Exercises 33
SI
Chapter 2 Test 37
Cumulative Review of Chapters 1 and 2 39
Chapter 3 Using Slope to Graph Linear Equations
VE
3.1 Graphing Equations of the Forms y = mx + b and x = a 42
3.2 Graphing Linear Models; Unit Analysis 48
3.3 Slope of a Line 54
3.4 Using Slope to Graph Linear Equations 56
3.5 Rate of Change 63
G
Chapter 3 Review Exercises 69
Chapter 3 Test 75
Chapter 4 Simplifying Expressions and Solving Equations
R
4.1 Simplifying Expressions 79
4.2 Simplifying More Expressions 81
4.3 Solving Linear Equations in One Variable 83
AD
4.4 Solving More Linear Equations in One Variable 88
4.5 Comparing Expressions and Equations 96
4.6 Formulas 99
Chapter 4 Review Exercises 104
Chapter 4 Test 110
Cumulative Review of Chapters 1–4 113
ES
i
, Chapter 5 Linear Equations in Two Variables and Linear Inequalities
in One Variable
M
5.1 Graphing Linear Equations in Two Variables 118
5.2 Finding Equations of Lines 126
5.3 Finding Equations of Linear Models 133
5.4 Using Equations of Linear Models to Make Estimates and Predictions 139
PR
5.5 Solving Linear Inequalities in One Variable 145
Chapter 5 Review Exercises 150
Chapter 5 Test 162
Chapter 6 Systems of Linear Equations and Systems of Linear
Inequalities
ES
6.1 Using Graphs and Tables to Solve Systems 166
6.2 Using Substitution to Solve Systems 171
6.3 Using Elimination to Solve Systems 176
6.4 Using Systems to Model Data 185
6.5 Perimeter, Value, Interest, and Mixture Problems 190
6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 197
SI
Chapter 6 Review Exercises 205
Chapter 6 Test 217
Cumulative Review of Chapters 1–6 223
Chapter 7 Polynomials and Properties of Exponents
VE
7.1 Graphing Quadratic Equations 232
7.2 Quadratic Models 236
7.3 Adding and Subtracting Polynomials 239
7.4 Multiplying Polynomials 242
7.5 Powers of Polynomials; Product of Binomial Conjugates 246
G
7.6 Properties of Exponents 250
7.7 Negative-Integer Exponents 252
7.8 Dividing Polynomials 255
Chapter 7 Review Exercises 260
R
Chapter 7 Test 266
Chapter 8 Factoring Polynomials and Solving Polynomial Equations
AD
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares 269
8.2 Factoring Out the GCF; Factoring by Grouping 273
8.3 Factoring Trinomials of the Form ax2 + bx + c 276
8.4 Sums and Differences of Cubes; A Factoring Strategy 286
8.5 Using Factoring to Solve Polynomial Equations 290
8.6 Using Factoring to Make Predictions with Quadratic Models 295
ES
Chapter 8 Review Exercises 299
Chapter 8 Test 305
Cumulative Review of Chapters 1–8 308
ii
M
SOLUTIONS MANUAL
PR
DIACRITECH
E LEMENTARY A LGEBRA :
ES
G RAPHS AND A UTHENTIC
A PPLICATIONS
SI
THIRD EDITION
VE
G
Jay Lehmann
College of San Mateo
R
AD
ES
,M
PR
ES
SI
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher
make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this
VE
book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with,
or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2019, 2015, 2011 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
G
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
R
publisher. Printed in the United States of America.
AD
ES
ISBN-13: 978-0-13-479533-1
ISBN-10: 0-13-479533-4
, Contents
Chapter 1 Introduction to Modeling
M
1.1 Variables and Constants 1
1.2 Scatterplots 3
1.3 Exact Linear Relationships 5
PR
1.4 Approximate Linear Relationships 8
Chapter 1 Review Exercises 12
Chapter 1 Test 15
Chapter 2 Operations and Expressions
ES
2.1 Expressions 17
2.2 Operations with Fractions 18
2.3 Absolute Value and Adding Real Numbers 21
2.4 Change in a Quantity and Subtracting Real Numbers 24
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers 27
2.6 Exponents and Order of Operations 30
Chapter 2 Review Exercises 33
SI
Chapter 2 Test 37
Cumulative Review of Chapters 1 and 2 39
Chapter 3 Using Slope to Graph Linear Equations
VE
3.1 Graphing Equations of the Forms y = mx + b and x = a 42
3.2 Graphing Linear Models; Unit Analysis 48
3.3 Slope of a Line 54
3.4 Using Slope to Graph Linear Equations 56
3.5 Rate of Change 63
G
Chapter 3 Review Exercises 69
Chapter 3 Test 75
Chapter 4 Simplifying Expressions and Solving Equations
R
4.1 Simplifying Expressions 79
4.2 Simplifying More Expressions 81
4.3 Solving Linear Equations in One Variable 83
AD
4.4 Solving More Linear Equations in One Variable 88
4.5 Comparing Expressions and Equations 96
4.6 Formulas 99
Chapter 4 Review Exercises 104
Chapter 4 Test 110
Cumulative Review of Chapters 1–4 113
ES
i
, Chapter 5 Linear Equations in Two Variables and Linear Inequalities
in One Variable
M
5.1 Graphing Linear Equations in Two Variables 118
5.2 Finding Equations of Lines 126
5.3 Finding Equations of Linear Models 133
5.4 Using Equations of Linear Models to Make Estimates and Predictions 139
PR
5.5 Solving Linear Inequalities in One Variable 145
Chapter 5 Review Exercises 150
Chapter 5 Test 162
Chapter 6 Systems of Linear Equations and Systems of Linear
Inequalities
ES
6.1 Using Graphs and Tables to Solve Systems 166
6.2 Using Substitution to Solve Systems 171
6.3 Using Elimination to Solve Systems 176
6.4 Using Systems to Model Data 185
6.5 Perimeter, Value, Interest, and Mixture Problems 190
6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 197
SI
Chapter 6 Review Exercises 205
Chapter 6 Test 217
Cumulative Review of Chapters 1–6 223
Chapter 7 Polynomials and Properties of Exponents
VE
7.1 Graphing Quadratic Equations 232
7.2 Quadratic Models 236
7.3 Adding and Subtracting Polynomials 239
7.4 Multiplying Polynomials 242
7.5 Powers of Polynomials; Product of Binomial Conjugates 246
G
7.6 Properties of Exponents 250
7.7 Negative-Integer Exponents 252
7.8 Dividing Polynomials 255
Chapter 7 Review Exercises 260
R
Chapter 7 Test 266
Chapter 8 Factoring Polynomials and Solving Polynomial Equations
AD
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares 269
8.2 Factoring Out the GCF; Factoring by Grouping 273
8.3 Factoring Trinomials of the Form ax2 + bx + c 276
8.4 Sums and Differences of Cubes; A Factoring Strategy 286
8.5 Using Factoring to Solve Polynomial Equations 290
8.6 Using Factoring to Make Predictions with Quadratic Models 295
ES
Chapter 8 Review Exercises 299
Chapter 8 Test 305
Cumulative Review of Chapters 1–8 308
ii
