VE
R
INSTRUCTOR’S
IF
IE
SOLUTIONS MANUAL
D
BR
MATH MADE VISIBLE
AI
E LEMENTARY A LGEBRA
N
BO
FOR C OLLEGE S TUDENTS
O
TENTH EDITION
ST
ER
Allen R. Angel
Monroe Community College
Dennis C. Runde
State College of Florida
VERIFIEDBRAINBOOSTER
, VE
R
IF
IE
D
BR
AI
N
BO
O
ST
ER
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.
Copyright © 2019, 2015, 2011 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
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.
ISBN-13: 978-0-13-476662-1
ISBN-10: 0-13-476662-8
VERIFIEDBRAINBOOSTER
, VE
R
Elementary Algebra For College Students
Table of Contents
IF
1. Real Numbers .............................................................................................................................1
1.1 Study Skills for Success in Mathematics .......................................................................1
IE
1.2 Problem Solving.............................................................................................................1
1.3 Fractions .........................................................................................................................6
D
1.4 The Real Number System ............................................................................................15
BR
1.5 Inequalities and Absolute Value ..................................................................................17
Mid-Chapter Test: Sections 1.1–1.5 ......................................................................21
1.6 Addition of Real Numbers ...........................................................................................22
AI
1.7 Subtraction of Real Numbers .......................................................................................29
1.8 Multiplication and Division of Real Numbers .............................................................36
N
1.9 Exponents, Parentheses, and the Order of Operations .................................................42
BO
1.10 Properties of the Real Number System ......................................................................50
Review Exercises ...............................................................................................................52
Practice Test .......................................................................................................................57
O
2. Solving Linear Equations and Inequalities ...........................................................................59
2.1 Combining Like Terms ................................................................................................59
ST
2.2 The Addition Property of Equality ..............................................................................64
2.3 The Multiplication Property of Equality ......................................................................71
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation............79
ER
Mid-Chapter Test: Sections 2.1–2.4 ......................................................................89
2.5 Solving Linear Equations with the Variable on Both Sides of the Equation ...............91
2.6 Formulas ....................................................................................................................101
2.7 Ratios and Proportions ...............................................................................................112
2.8 Inequalities in One Variable ......................................................................................120
Review Exercises .............................................................................................................128
Practice Test .....................................................................................................................138
Cumulative Review Test ..................................................................................................141
3. Applications of Algebra .........................................................................................................143
3.1 Changing Application Problems into Equations ........................................................143
3.2 Solving Application Problems ...................................................................................147
Mid-Chapter Test: Sections 3.1–3.2 ....................................................................154
3.3 Geometric Problems...................................................................................................155
3.4 Motion, Money, and Mixture Problems .....................................................................159
Review Exercises .............................................................................................................170
Practice Test .....................................................................................................................175
Cumulative Review Test ..................................................................................................178
4. Exponents and Polynomials ..................................................................................................180
4.1 Exponents ...................................................................................................................180
4.2 Negative Exponents ...................................................................................................187
4.3 Scientific Notation .....................................................................................................193
Mid-Chapter Test: Sections 4.1–4.3 ....................................................................199
4.4 Addition and Subtraction of Polynomials ..................................................................200
4.5 Multiplication of Polynomials ...................................................................................205
4.6 Division of Polynomials ............................................................................................212
VERIFIEDBRAINBOOSTER
, VE
R
Review Exercises .............................................................................................................219
Practice Test .....................................................................................................................225
IF
Cumulative Review Test ..................................................................................................226
5. Factoring .................................................................................................................................229
IE
5.1 Factoring a Monomial from a Polynomial .................................................................229
5.2 Factoring by Grouping ...............................................................................................233
D
5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 ...............................................237
BR
5.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 ...............................................240
Mid-Chapter Test: Sections 5.1–5.4 ....................................................................243
5.5 Special Factoring Formulas and a General Review of Factoring ..............................244
AI
5.6 Solving Quadratic Equations Using Factoring ..........................................................249
5.7 Applications of Quadratic Equations .........................................................................254
N
Review Exercises .............................................................................................................261
BO
Practice Test .....................................................................................................................267
Cumulative Review Test ..................................................................................................268
6. Rational Expressions and Equations....................................................................................271
O
6.1 Simplifying Rational Expressions..............................................................................271
6.2 Multiplication and Division of Rational Expressions ................................................276
ST
6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and
Finding the Least Common Denominator........................................................................285
6.4 Addition and Subtraction of Rational Expressions ....................................................294
ER
Mid-Chapter Test: Sections 6.1–6.4 ....................................................................305
6.5 Complex Fractions .....................................................................................................307
6.6 Solving Rational Equations........................................................................................313
6.7 Rational Equations: Applications and Problem Solving ............................................337
6.8 Variation ....................................................................................................................345
Review Exercises .............................................................................................................350
Practice Test .....................................................................................................................358
Cumulative Review Test ..................................................................................................360
7. Graphing Linear Equations ..................................................................................................363
7.1 The Cartesian Coordinate System and Linear Equations in Two Variables ..............363
7.2 Graphing Linear Equations ........................................................................................366
7.3 Slope of a Line ...........................................................................................................376
Mid-Chapter Test: Sections 7.1–7.3 ....................................................................379
7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation ...................................380
7.5 Graphing Linear Inequalities .....................................................................................387
7.6 Functions ....................................................................................................................391
Review Exercises .............................................................................................................395
Practice Test .....................................................................................................................399
Cumulative Review Test ..................................................................................................401
8. Systems of Linear Equations ................................................................................................404
8.1 Solving Systems of Equations Graphically................................................................404
8.2 Solving Systems of Equations by Substitution ..........................................................412
8.3 Solving Systems of Equations by the Addition Method ............................................421
Mid-Chapter Test: Sections 8.1–8.3 ....................................................................435
8.4 Systems of Equations: Applications and Problem Solving........................................438
VERIFIEDBRAINBOOSTER
R
INSTRUCTOR’S
IF
IE
SOLUTIONS MANUAL
D
BR
MATH MADE VISIBLE
AI
E LEMENTARY A LGEBRA
N
BO
FOR C OLLEGE S TUDENTS
O
TENTH EDITION
ST
ER
Allen R. Angel
Monroe Community College
Dennis C. Runde
State College of Florida
VERIFIEDBRAINBOOSTER
, VE
R
IF
IE
D
BR
AI
N
BO
O
ST
ER
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.
Copyright © 2019, 2015, 2011 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
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.
ISBN-13: 978-0-13-476662-1
ISBN-10: 0-13-476662-8
VERIFIEDBRAINBOOSTER
, VE
R
Elementary Algebra For College Students
Table of Contents
IF
1. Real Numbers .............................................................................................................................1
1.1 Study Skills for Success in Mathematics .......................................................................1
IE
1.2 Problem Solving.............................................................................................................1
1.3 Fractions .........................................................................................................................6
D
1.4 The Real Number System ............................................................................................15
BR
1.5 Inequalities and Absolute Value ..................................................................................17
Mid-Chapter Test: Sections 1.1–1.5 ......................................................................21
1.6 Addition of Real Numbers ...........................................................................................22
AI
1.7 Subtraction of Real Numbers .......................................................................................29
1.8 Multiplication and Division of Real Numbers .............................................................36
N
1.9 Exponents, Parentheses, and the Order of Operations .................................................42
BO
1.10 Properties of the Real Number System ......................................................................50
Review Exercises ...............................................................................................................52
Practice Test .......................................................................................................................57
O
2. Solving Linear Equations and Inequalities ...........................................................................59
2.1 Combining Like Terms ................................................................................................59
ST
2.2 The Addition Property of Equality ..............................................................................64
2.3 The Multiplication Property of Equality ......................................................................71
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation............79
ER
Mid-Chapter Test: Sections 2.1–2.4 ......................................................................89
2.5 Solving Linear Equations with the Variable on Both Sides of the Equation ...............91
2.6 Formulas ....................................................................................................................101
2.7 Ratios and Proportions ...............................................................................................112
2.8 Inequalities in One Variable ......................................................................................120
Review Exercises .............................................................................................................128
Practice Test .....................................................................................................................138
Cumulative Review Test ..................................................................................................141
3. Applications of Algebra .........................................................................................................143
3.1 Changing Application Problems into Equations ........................................................143
3.2 Solving Application Problems ...................................................................................147
Mid-Chapter Test: Sections 3.1–3.2 ....................................................................154
3.3 Geometric Problems...................................................................................................155
3.4 Motion, Money, and Mixture Problems .....................................................................159
Review Exercises .............................................................................................................170
Practice Test .....................................................................................................................175
Cumulative Review Test ..................................................................................................178
4. Exponents and Polynomials ..................................................................................................180
4.1 Exponents ...................................................................................................................180
4.2 Negative Exponents ...................................................................................................187
4.3 Scientific Notation .....................................................................................................193
Mid-Chapter Test: Sections 4.1–4.3 ....................................................................199
4.4 Addition and Subtraction of Polynomials ..................................................................200
4.5 Multiplication of Polynomials ...................................................................................205
4.6 Division of Polynomials ............................................................................................212
VERIFIEDBRAINBOOSTER
, VE
R
Review Exercises .............................................................................................................219
Practice Test .....................................................................................................................225
IF
Cumulative Review Test ..................................................................................................226
5. Factoring .................................................................................................................................229
IE
5.1 Factoring a Monomial from a Polynomial .................................................................229
5.2 Factoring by Grouping ...............................................................................................233
D
5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 ...............................................237
BR
5.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 ...............................................240
Mid-Chapter Test: Sections 5.1–5.4 ....................................................................243
5.5 Special Factoring Formulas and a General Review of Factoring ..............................244
AI
5.6 Solving Quadratic Equations Using Factoring ..........................................................249
5.7 Applications of Quadratic Equations .........................................................................254
N
Review Exercises .............................................................................................................261
BO
Practice Test .....................................................................................................................267
Cumulative Review Test ..................................................................................................268
6. Rational Expressions and Equations....................................................................................271
O
6.1 Simplifying Rational Expressions..............................................................................271
6.2 Multiplication and Division of Rational Expressions ................................................276
ST
6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and
Finding the Least Common Denominator........................................................................285
6.4 Addition and Subtraction of Rational Expressions ....................................................294
ER
Mid-Chapter Test: Sections 6.1–6.4 ....................................................................305
6.5 Complex Fractions .....................................................................................................307
6.6 Solving Rational Equations........................................................................................313
6.7 Rational Equations: Applications and Problem Solving ............................................337
6.8 Variation ....................................................................................................................345
Review Exercises .............................................................................................................350
Practice Test .....................................................................................................................358
Cumulative Review Test ..................................................................................................360
7. Graphing Linear Equations ..................................................................................................363
7.1 The Cartesian Coordinate System and Linear Equations in Two Variables ..............363
7.2 Graphing Linear Equations ........................................................................................366
7.3 Slope of a Line ...........................................................................................................376
Mid-Chapter Test: Sections 7.1–7.3 ....................................................................379
7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation ...................................380
7.5 Graphing Linear Inequalities .....................................................................................387
7.6 Functions ....................................................................................................................391
Review Exercises .............................................................................................................395
Practice Test .....................................................................................................................399
Cumulative Review Test ..................................................................................................401
8. Systems of Linear Equations ................................................................................................404
8.1 Solving Systems of Equations Graphically................................................................404
8.2 Solving Systems of Equations by Substitution ..........................................................412
8.3 Solving Systems of Equations by the Addition Method ............................................421
Mid-Chapter Test: Sections 8.1–8.3 ....................................................................435
8.4 Systems of Equations: Applications and Problem Solving........................................438
VERIFIEDBRAINBOOSTER
