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Elementary and Intermediate Algebra for College Students 5th Edition by Allen R. Angel SOLUTION
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INSTRUCTOR’SSOLUTIONS MANUAL
MATH MADE VISIBLE
E LEMENTARY & I NTERMEDIATE
A LGEBRA
FOR C OLLEGE S TUDENTS
FIFTH EDITION
Allen R. Angel
Monroe Community College
Dennis C. Runde
State College of Florida
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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
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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: 978-0-13-479515-7
ISBN-10: 0-13-479515-6
,Elementary and Intermediate Algebra For College Students
Table of Contents
1. Real Numbers ............................................................................................................................ 1
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
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
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
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
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
3.2 Solving Application Problems .................................................................................. 136
Mid-Chapter Test: Sections 3.1–3.2 ................................................................... 143
3.3 Geometric Problems.................................................................................................. 144
3.4 Motion, Money, and Mixture Problems.................................................................... 148
Review Exercises ............................................................................................................ 158
Practice Test .................................................................................................................... 163
Cumulative Review Test ................................................................................................. 165
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
Review Exercises ............................................................................................................ 191
Practice Test .................................................................................................................... 194
Cumulative Review Test ................................................................................................. 196
, 5. Exponents and Polynomials ................................................................................................. 198
5.1 Exponents.................................................................................................................. 198
5.2 Negative Exponents .................................................................................................. 204
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
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
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
6.7 Applications of Quadratic Equations ........................................................................ 272
Review Exercises ............................................................................................................ 278
Practice Test .................................................................................................................... 284
Cumulative Review Test ................................................................................................. 285
7. Rational Expressions and Equations................................................................................... 288
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
7.5 Complex Fractions .................................................................................................... 324
7.6 Solving Rational Equations....................................................................................... 330
7.7 Rational Equations: Applications and Problem Solving........................................... 352
7.8 Variation ................................................................................................................... 360
Review Exercises ............................................................................................................ 368
Practice Test .................................................................................................................... 377
Cumulative Review Test ................................................................................................. 379
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