INSTRUCTOR’S
SOLUTIONS MANUAL
DIACRITECH
N
E LEMENTARY
& I NTERMEDIATE A LGEBRA :
U
F UNCTIONS AND A UTHENTIC
R
A PPLICATIONS
SE
THIRD EDITION
D
O
Jay Lehmann
C
College of San Mateo
S
,N
U
R
SE
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
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.
D
Copyright © 2019, 2015, 2011 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
O
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
publisher. Printed in the United States of America.
C
S
ISBN-13: 978-0-13-478018-4
ISBN-10: 0-13-478018-3
, Contents
Chapter 1 Introduction to Modeling
1.1 Variables and Constants 1
1.2 Scatterplots 3
1.3 Exact Linear Relationships 5
1.4 Approximate Linear Relationships 8
Chapter 1 Review Exercises 12
Chapter 1 Test 15
N
Chapter 2 Operations and Expressions
2.1 Expressions 18
U
2.2 Operations with Fractions 19
2.3 Absolute Value and Adding Real Numbers 22
2.4 Change in a Quantity and Subtracting Real Numbers 25
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers 28
R
2.6 Exponents and Order of Operations 31
Chapter 2 Review Exercises 34
Chapter 2 Test 38
Cumulative Review of Chapters 1 and 2 40
SE
Chapter 3 Using Slope to Graph Linear Equations
3.1 Graphing Equations of the Forms y = mx + b and x = a 43
3.2 Graphing Linear Models; Unit Analysis 49
D
3.3 Slope of a Line 55
3.4 Using Slope to Graph Linear Equations 58
3.5 Rate of Change 65
Chapter 3 Review Exercises 71
O
Chapter 3 Test 77
Chapter 4 Simplifying Expressions and Solving Equations
C
4.1 Simplifying Expressions 81
4.2 Simplifying More Expressions 83
4.3 Solving Linear Equations in One Variable 85
S
4.4 Solving More Linear Equations in One Variable 90
4.5 Comparing Expressions and Equations 98
4.6 Formulas 101
Chapter 4 Review Exercises 106
Chapter 4 Test 112
Cumulative Review of Chapters 1–4 115
iii
, Chapter 5 Linear Functions and Linear Inequalities in One Variable
5.1 Graphing Linear Equations 120
5.2 Functions 129
5.3 Function Notation 131
5.4 Finding Linear Equations 134
5.5 Finding Equations of Linear Models 141
5.6 Using Function Notation with Linear Models to Make Estimates and Predictions 147
5.7 Solving Linear Inequalities in One Variable 154
Chapter 5 Review Exercises 160
Chapter 5 Test 170
N
Chapter 6 Systems of Linear Equations and Systems of Linear
Inequalities
U
6.1 Using Graphs and Tables to Solve Systems 175
6.2 Using Substitution to Solve Systems 181
6.3 Using Elimination to Solve Systems 187
R
6.4 Using Systems to Model Data 196
6.5 Perimeter, Value, Interest, and Mixture Problems 202
6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 211
Chapter 6 Review Exercises 219
SE
Chapter 6 Test 233
Cumulative Review of Chapters 1–6 240
Chapter 7 Polynomial Functions and Properties of Exponents
7.1 Adding and Subtracting Polynomial Expressions and Functions 249
D
7.2 Multiplying Polynomial Expressions and Functions 252
7.3 Powers of Polynomials; Product of Binomial Conjugates 256
7.4 Properties of Exponents 260
7.5 Dividing Polynomials: Long Division and Synthetic Division 262
O
Chapter 7 Review Exercises 267
Chapter 7 Test 271
Making Sure You’re Ready for Intermediate Algebra: A Review of Chapters 1–7 272
C
Chapter 8 Factoring Polynomials and Solving Polynomial Equations
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares 280
S
8.2 Factoring Out the GCF; Factoring by Grouping 284
8.3 Factoring Trinomials of the Form ax2 + bx + c 287
8.4 Sums and Differences of Cubes; A Factoring Strategy 298
8.5 Using Factoring to Solve Polynomial Equations 302
8.6 Using Factoring to Make Predictions with Quadratic Models 305
Chapter 8 Review Exercises 310
Chapter 8 Test 316
Making Sure You’re Ready for Intermediate Algebra: A Review of Chapters 1–8 318
iv
SOLUTIONS MANUAL
DIACRITECH
N
E LEMENTARY
& I NTERMEDIATE A LGEBRA :
U
F UNCTIONS AND A UTHENTIC
R
A PPLICATIONS
SE
THIRD EDITION
D
O
Jay Lehmann
C
College of San Mateo
S
,N
U
R
SE
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
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.
D
Copyright © 2019, 2015, 2011 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
O
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
publisher. Printed in the United States of America.
C
S
ISBN-13: 978-0-13-478018-4
ISBN-10: 0-13-478018-3
, Contents
Chapter 1 Introduction to Modeling
1.1 Variables and Constants 1
1.2 Scatterplots 3
1.3 Exact Linear Relationships 5
1.4 Approximate Linear Relationships 8
Chapter 1 Review Exercises 12
Chapter 1 Test 15
N
Chapter 2 Operations and Expressions
2.1 Expressions 18
U
2.2 Operations with Fractions 19
2.3 Absolute Value and Adding Real Numbers 22
2.4 Change in a Quantity and Subtracting Real Numbers 25
2.5 Ratios, Percents, and Multiplying and Dividing Real Numbers 28
R
2.6 Exponents and Order of Operations 31
Chapter 2 Review Exercises 34
Chapter 2 Test 38
Cumulative Review of Chapters 1 and 2 40
SE
Chapter 3 Using Slope to Graph Linear Equations
3.1 Graphing Equations of the Forms y = mx + b and x = a 43
3.2 Graphing Linear Models; Unit Analysis 49
D
3.3 Slope of a Line 55
3.4 Using Slope to Graph Linear Equations 58
3.5 Rate of Change 65
Chapter 3 Review Exercises 71
O
Chapter 3 Test 77
Chapter 4 Simplifying Expressions and Solving Equations
C
4.1 Simplifying Expressions 81
4.2 Simplifying More Expressions 83
4.3 Solving Linear Equations in One Variable 85
S
4.4 Solving More Linear Equations in One Variable 90
4.5 Comparing Expressions and Equations 98
4.6 Formulas 101
Chapter 4 Review Exercises 106
Chapter 4 Test 112
Cumulative Review of Chapters 1–4 115
iii
, Chapter 5 Linear Functions and Linear Inequalities in One Variable
5.1 Graphing Linear Equations 120
5.2 Functions 129
5.3 Function Notation 131
5.4 Finding Linear Equations 134
5.5 Finding Equations of Linear Models 141
5.6 Using Function Notation with Linear Models to Make Estimates and Predictions 147
5.7 Solving Linear Inequalities in One Variable 154
Chapter 5 Review Exercises 160
Chapter 5 Test 170
N
Chapter 6 Systems of Linear Equations and Systems of Linear
Inequalities
U
6.1 Using Graphs and Tables to Solve Systems 175
6.2 Using Substitution to Solve Systems 181
6.3 Using Elimination to Solve Systems 187
R
6.4 Using Systems to Model Data 196
6.5 Perimeter, Value, Interest, and Mixture Problems 202
6.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables 211
Chapter 6 Review Exercises 219
SE
Chapter 6 Test 233
Cumulative Review of Chapters 1–6 240
Chapter 7 Polynomial Functions and Properties of Exponents
7.1 Adding and Subtracting Polynomial Expressions and Functions 249
D
7.2 Multiplying Polynomial Expressions and Functions 252
7.3 Powers of Polynomials; Product of Binomial Conjugates 256
7.4 Properties of Exponents 260
7.5 Dividing Polynomials: Long Division and Synthetic Division 262
O
Chapter 7 Review Exercises 267
Chapter 7 Test 271
Making Sure You’re Ready for Intermediate Algebra: A Review of Chapters 1–7 272
C
Chapter 8 Factoring Polynomials and Solving Polynomial Equations
8.1 Factoring Trinomials of the Form x2 + bx + c and Differences of Two Squares 280
S
8.2 Factoring Out the GCF; Factoring by Grouping 284
8.3 Factoring Trinomials of the Form ax2 + bx + c 287
8.4 Sums and Differences of Cubes; A Factoring Strategy 298
8.5 Using Factoring to Solve Polynomial Equations 302
8.6 Using Factoring to Make Predictions with Quadratic Models 305
Chapter 8 Review Exercises 310
Chapter 8 Test 316
Making Sure You’re Ready for Intermediate Algebra: A Review of Chapters 1–8 318
iv
