SOLUTIONS MANUAL MATH MADE VISIBLE ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS TENTH EDITION

SOLUTIONS MANUAL MATH MADE VISIBLE ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS TENTH EDITION Allen R. Angel Monroe Community College Dennis C. Runde State College of FloridaThe 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: 0-13-476662-8Elementary 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 .............................................................36 1.9 Exponents, Parentheses, and the Order of Operations .................................................42 1.10 Properties of the Real Number System ......................................................................50 Review Exercises ...............................................................................................................52 Practice Test .......................................................................................................................57 2. Solving Linear Equations and Inequalities ...........................................................................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 ...............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 ............................................................................................212Review Exercises .............................................................................................................219 Practice Test .....................................................................................................................225 Cumulative Review Test ..................................................................................................226 5. Factoring .................................................................................................................................229 5.1 Factoring a Monomial from a Polynomial .................................................................229 5.2 Factoring by Grouping ...............................................................................................233 5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 ...............................................237 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 5.6 Solving Quadratic Equations Using Factoring ..........................................................249 5.7 Applications of Quadratic Equations .........................................................................254 Review Exercises .............................................................................................................261 Practice Test .....................................................................................................................267 Cumulative Review Test ..................................................................................................268 6. Rational Expressions and Equations ....................................................................................271 6.1 Simplifying Rational Expressions..............................................................................271 6.2 Multiplication and Division of Rational Expressions ................................................276 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 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........................................4388.5 Solving Systems of Linear Inequalities .....................................................................451 Review Exercises .............................................................................................................452 Practice Test .....................................................................................................................459 Cumulative Review Test ..................................................................................................463 9. Roots and Radicals .................................................................................................................465 9.1 Evaluating Square Roots ............................................................................................465 9.2 Simplifying Square Roots ..........................................................................................468 9.3 Adding, Subtracting, and Multiplying Square Roots .................................................473 9.4 Dividing Square Roots ...............................................................................................479 Mid-Chapter Test: Sections 9.1–9.4 ....................................................................488 9.5 Solving Radical Equations .........................................................................................489 9.6 Radicals: Applications and Problem Solving ............................................................499 9.7 Higher Roots and Rational Exponents .......................................................................503 Review Exercises .............................................................................................................506 Practice Test .....................................................................................................................512 Cumulative Review Test ..................................................................................................514 10. Quadratic Equations ............................................................................................................516 10.1 The Square Root Property ........................................................................................516 10.2 Solving Quadratic Equations by Completing the Square ........................................522 10.3 Solving Quadratic Equations by the Quadratic Formula .........................................536 Mid-Chapter Test: Sections 10.1–10.3 ................................................................552 10.4 Graphing Quadratic Equations .................................................................................555 10.5 Complex Numbers ...................................................................................................575 Review Exercises .............................................................................................................580 Practice Test .....................................................................................................................598 Cumulative Review Test ..........................................................