INSTRUCTOR’S
M
SOLUTIONS MANUAL
PR
MATH MADE VISIBLE
E LEMENTARY & I NTERMEDIATE
ES
A LGEBRA
FOR C OLLEGE S TUDENTS
SI
FIFTH EDITION
VE
Allen R. Angel
G
Monroe Community College
R
Dennis C. Runde
State College of Florida
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 book. The author and
VE
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 publisher.
R
Printed in the United States of America.
AD
ES
ISBN-13: 978-0-13-479515-7
ISBN-10: 0-13-479515-6
, Elementary and Intermediate Algebra For College Students
Table of Contents
1. Real Numbers ............................................................................................................................ 1
M
1.1 Study Skills for Success in Mathematics ...................................................................... 1
1.2 Problem Solving ........................................................................................................... 1
1.3 Fractions........................................................................................................................ 6
1.4 The Real Number System ........................................................................................... 15
PR
1.5 Inequalities and Absolute Value ................................................................................. 17
Mid-Chapter Test: Sections 1.1–1.5 ..................................................................... 21
1.6 Addition of Real Numbers .......................................................................................... 22
1.7 Subtraction of Real Numbers ...................................................................................... 29
1.8 Multiplication and Division of Real Numbers ............................................................ 35
1.9 Exponents, Parentheses, and the Order of Operations ................................................ 41
ES
1.10 Properties of the Real Number System ..................................................................... 50
Review Exercises ............................................................................................................. 52
Practice Test ...................................................................................................................... 57
2. Solving Linear Equations ....................................................................................................... 59
2.1 Combining Like Terms ............................................................................................... 59
2.2 The Addition Property of Equality ............................................................................. 64
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2.3 The Multiplication Property of Equality ..................................................................... 71
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation........... 79
Mid-Chapter Test: Sections 2.1–2.4 ..................................................................... 89
2.5 Solving Linear Equations with the Variable on Both Sides of the Equation .............. 90
2.6 Formulas ................................................................................................................... 101
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2.7 Ratios and Proportions .............................................................................................. 112
Review Exercises ............................................................................................................ 119
Practice Test .................................................................................................................... 128
Cumulative Review Test ................................................................................................. 130
3. Applications of Algebra ........................................................................................................ 132
3.1 Changing Application Problems into Equations ....................................................... 132
G
3.2 Solving Application Problems .................................................................................. 136
Mid-Chapter Test: Sections 3.1–3.2 ................................................................... 143
3.3 Geometric Problems.................................................................................................. 144
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3.4 Motion, Money, and Mixture Problems.................................................................... 148
Review Exercises ............................................................................................................ 158
Practice Test .................................................................................................................... 163
Cumulative Review Test ................................................................................................. 165
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4. Graphing Linear Equations ................................................................................................. 168
4.1 The Cartesian Coordinate System and Linear Equations in Two Variables ............. 168
4.2 Graphing Linear Equations ....................................................................................... 171
4.3 Slope of a Line .......................................................................................................... 180
Mid-Chapter Test: Sections 4.1–4.3 ................................................................... 183
4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation .................................. 185
ES
Review Exercises ............................................................................................................ 191
Practice Test .................................................................................................................... 194
Cumulative Review Test ................................................................................................. 196
, 5. Exponents and Polynomials ................................................................................................. 198
5.1 Exponents.................................................................................................................. 198
5.2 Negative Exponents .................................................................................................. 204
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5.3 Scientific Notation .................................................................................................... 211
Mid-Chapter Test: Sections 5.1–5.3 ................................................................... 217
5.4 Addition and Subtraction of Polynomials ................................................................. 217
5.5 Multiplication of Polynomials .................................................................................. 223
PR
5.6 Division of Polynomials ........................................................................................... 230
Review Exercises ............................................................................................................ 237
Practice Test .................................................................................................................... 243
Cumulative Review Test ................................................................................................. 245
6. Factoring ................................................................................................................................ 247
6.1 Factoring a Monomial from a Polynomial ................................................................ 247
ES
6.2 Factoring by Grouping .............................................................................................. 251
6.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 .............................................. 255
6.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 .............................................. 258
Mid-Chapter Test: Sections 6.1–6.4 ................................................................... 261
6.5 Special Factoring Formulas and a General Review of Factoring ............................. 262
6.6 Solving Quadratic Equations Using Factoring ......................................................... 267
SI
6.7 Applications of Quadratic Equations ........................................................................ 272
Review Exercises ............................................................................................................ 278
Practice Test .................................................................................................................... 284
Cumulative Review Test ................................................................................................. 285
7. Rational Expressions and Equations................................................................................... 288
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7.1 Simplifying Rational Expressions............................................................................. 288
7.2 Multiplication and Division of Rational Expressions ............................................... 293
7.3 Addition and Subtraction of Rational Expressions with a Common
Denominator and Determining the Least Common Denominator ............................ 301
7.4 Addition and Subtraction of Rational Expressions ................................................... 310
Mid-Chapter Test: Sections 7.1–7.4 ................................................................... 322
G
7.5 Complex Fractions .................................................................................................... 324
7.6 Solving Rational Equations....................................................................................... 330
7.7 Rational Equations: Applications and Problem Solving........................................... 352
R
7.8 Variation ................................................................................................................... 360
Review Exercises ............................................................................................................ 368
Practice Test .................................................................................................................... 377
Cumulative Review Test ................................................................................................. 379
AD
ES
M
SOLUTIONS MANUAL
PR
MATH MADE VISIBLE
E LEMENTARY & I NTERMEDIATE
ES
A LGEBRA
FOR C OLLEGE S TUDENTS
SI
FIFTH EDITION
VE
Allen R. Angel
G
Monroe Community College
R
Dennis C. Runde
State College of Florida
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 book. The author and
VE
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 publisher.
R
Printed in the United States of America.
AD
ES
ISBN-13: 978-0-13-479515-7
ISBN-10: 0-13-479515-6
, Elementary and Intermediate Algebra For College Students
Table of Contents
1. Real Numbers ............................................................................................................................ 1
M
1.1 Study Skills for Success in Mathematics ...................................................................... 1
1.2 Problem Solving ........................................................................................................... 1
1.3 Fractions........................................................................................................................ 6
1.4 The Real Number System ........................................................................................... 15
PR
1.5 Inequalities and Absolute Value ................................................................................. 17
Mid-Chapter Test: Sections 1.1–1.5 ..................................................................... 21
1.6 Addition of Real Numbers .......................................................................................... 22
1.7 Subtraction of Real Numbers ...................................................................................... 29
1.8 Multiplication and Division of Real Numbers ............................................................ 35
1.9 Exponents, Parentheses, and the Order of Operations ................................................ 41
ES
1.10 Properties of the Real Number System ..................................................................... 50
Review Exercises ............................................................................................................. 52
Practice Test ...................................................................................................................... 57
2. Solving Linear Equations ....................................................................................................... 59
2.1 Combining Like Terms ............................................................................................... 59
2.2 The Addition Property of Equality ............................................................................. 64
SI
2.3 The Multiplication Property of Equality ..................................................................... 71
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation........... 79
Mid-Chapter Test: Sections 2.1–2.4 ..................................................................... 89
2.5 Solving Linear Equations with the Variable on Both Sides of the Equation .............. 90
2.6 Formulas ................................................................................................................... 101
VE
2.7 Ratios and Proportions .............................................................................................. 112
Review Exercises ............................................................................................................ 119
Practice Test .................................................................................................................... 128
Cumulative Review Test ................................................................................................. 130
3. Applications of Algebra ........................................................................................................ 132
3.1 Changing Application Problems into Equations ....................................................... 132
G
3.2 Solving Application Problems .................................................................................. 136
Mid-Chapter Test: Sections 3.1–3.2 ................................................................... 143
3.3 Geometric Problems.................................................................................................. 144
R
3.4 Motion, Money, and Mixture Problems.................................................................... 148
Review Exercises ............................................................................................................ 158
Practice Test .................................................................................................................... 163
Cumulative Review Test ................................................................................................. 165
AD
4. Graphing Linear Equations ................................................................................................. 168
4.1 The Cartesian Coordinate System and Linear Equations in Two Variables ............. 168
4.2 Graphing Linear Equations ....................................................................................... 171
4.3 Slope of a Line .......................................................................................................... 180
Mid-Chapter Test: Sections 4.1–4.3 ................................................................... 183
4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation .................................. 185
ES
Review Exercises ............................................................................................................ 191
Practice Test .................................................................................................................... 194
Cumulative Review Test ................................................................................................. 196
, 5. Exponents and Polynomials ................................................................................................. 198
5.1 Exponents.................................................................................................................. 198
5.2 Negative Exponents .................................................................................................. 204
M
5.3 Scientific Notation .................................................................................................... 211
Mid-Chapter Test: Sections 5.1–5.3 ................................................................... 217
5.4 Addition and Subtraction of Polynomials ................................................................. 217
5.5 Multiplication of Polynomials .................................................................................. 223
PR
5.6 Division of Polynomials ........................................................................................... 230
Review Exercises ............................................................................................................ 237
Practice Test .................................................................................................................... 243
Cumulative Review Test ................................................................................................. 245
6. Factoring ................................................................................................................................ 247
6.1 Factoring a Monomial from a Polynomial ................................................................ 247
ES
6.2 Factoring by Grouping .............................................................................................. 251
6.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 .............................................. 255
6.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 .............................................. 258
Mid-Chapter Test: Sections 6.1–6.4 ................................................................... 261
6.5 Special Factoring Formulas and a General Review of Factoring ............................. 262
6.6 Solving Quadratic Equations Using Factoring ......................................................... 267
SI
6.7 Applications of Quadratic Equations ........................................................................ 272
Review Exercises ............................................................................................................ 278
Practice Test .................................................................................................................... 284
Cumulative Review Test ................................................................................................. 285
7. Rational Expressions and Equations................................................................................... 288
VE
7.1 Simplifying Rational Expressions............................................................................. 288
7.2 Multiplication and Division of Rational Expressions ............................................... 293
7.3 Addition and Subtraction of Rational Expressions with a Common
Denominator and Determining the Least Common Denominator ............................ 301
7.4 Addition and Subtraction of Rational Expressions ................................................... 310
Mid-Chapter Test: Sections 7.1–7.4 ................................................................... 322
G
7.5 Complex Fractions .................................................................................................... 324
7.6 Solving Rational Equations....................................................................................... 330
7.7 Rational Equations: Applications and Problem Solving........................................... 352
R
7.8 Variation ................................................................................................................... 360
Review Exercises ............................................................................................................ 368
Practice Test .................................................................................................................... 377
Cumulative Review Test ................................................................................................. 379
AD
ES
