INTRODUCTORY & INTERMEDIATE ALGEBRA Second Edition D. FRANKLIN WRIGHT CERRITOS COLLEGE Title Page.indd 15/28/2019 8:34:23 AMEditor: Nina Waldron Vice President, Development: Marcel Prevuznak Production Editor: Kara Roché Editorial Assistants: Jessica Ballance, Kaitlin Marley Layout: E. Jeevan Kumar, D. Kanthi, U. Nagesh, B. Syamprasad Copy Editors: A. Bhaskar Rao, Nicholas Boyer, B. Padmavathi, G. Ram Jagadish, Taylor Hamrick, Rebecca Hughes, K. Ramesh Narasimha, K.V.S. Anil, M. Prasanna Lakshmi, N. Narasimha Rao, U. Madhavi, U. Ravindra Kumar, Claudia Vance Contributors: Thomas Clark, Elizabeth Thomas, Melissa Turowski, Barry Wright, III Answer Key Editors: Vidya Bachina, Kirk Boyer, Peter Bull, Melissa Hecht, Caroline Holbrook, Taylor Jones, Saurabh Joshi, Eric Ketcham, Michael Lane, Joseph Miller, Pradeep Nagalla, Hemanth Nallagatla, Jacob Stauch, Yinliang Tan, Joseph Tracy, James von der Lieth, Colin Williams Art: Anushree C Bhattacharya, Ayvin Samonte Cover Art and Design: Jessica Cokins, Johnson Design Photograph Credits: iStockphoto.com and Digital Vision with the exception of: 71: Berners, edited by A. Winterberger; 126: NASA/JPL-Caltech; 195: Mark Wagner. A division of Quant Systems, Inc. 546 Long Point Road Mount Pleasant, SC 29464 Copyright © 2020, 2012 by Hawkes Learning Systems/Quant Systems, Inc. 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 consent of the publisher. Library of Congress Control Number: 2010901560 Printed in the United States of America 10 9 8 7 6 5 4 3 2 ISBN: 978-1-932628-77-7 AIE ISBN: 978-1-64277-192-3 Title Page.indd 25/16/2019 9:52:08 AMThis book is dedicated to the memory of Greg Hill Title Page.indd 310/8/2010 2:50:40 PMTitle Page.indd 410/8/2010 2:50:40 PMTABLE OF CONTENTS Preface xi Hawkes Learning Systems: Introductory & Intermediate Algebra xxiv 1.1 The Real Number Line and Absolute Value 2 1.2 Addition with Real Numbers 16 1.3 Subtraction with Real Numbers 21 1.4 Multiplication and Division with Real Numbers 31 1.5 Exponents, Prime Numbers, and LCM 42 1.6 Multiplication and Division with Fractions 54 1.7 Addition and Subtraction with Fractions 65 1.8 Order of Operations 73 1.9 Properties of Real Numbers 81 Chapter 1 Index of Key Ideas and Terms 87 Chapter 1 Chapter Review 94 Chapter 1 Chapter Test 99 2.1 Simplifying and Evaluating Algebraic Expressions 102 2.2 Translating English Phrases and Algebraic Expressions 110 2.3 Solving Linear Equations: x + b = c and ax = c 117 2.4 Solving Linear Equations: ax + b = c 127 2.5 Solving Linear Equations: ax + b = cx + d 134 2.6 Introduction to Problem Solving 142 2.7 Applications with Percent 153 Chapter 2 Index of Key Ideas and Terms 164 Chapter 2 Chapter Review 168 Chapter 2 Chapter Test 172 Chapters 1-2 Cumulative Review 174 Chapter 1 Real Numbers 1 Chapter 2 Algebraic Expressions, Linear Equations, and Applications 101 Table of Contents.indd 510/8/2010 2:51:25 PMvi TABLE OF CONTENTS 3.1 Working with Formulas 178 3.2 Formulas in Geometry 189 3.3 Applications: Distance-Rate-Time, Interest, Average 203 3.4 Linear Inequalities 214 3.5 Absolute Value Equations and Inequalities 229 Chapter 3 Index of Key Ideas and Terms 238 Chapter 3 Chapter Review 242 Chapter 3 Chapter Test 247 Chapters 1-3 Cumulative Review 250 4.1 The Cartesian Coordinate System 256 4.2 Graphing Linear Equations in Two Variables: Ax + By = C 273 4.3 The Slope-Intercept Form: y = mx + b 281 4.4 The Point-Slope Form: yymx x −=− () 11 297 4.5 Introduction to Functions and Function Notation 307 4.6 Graphing Linear Inequalities in Two Variables 326 Chapter 4 Index of Key Ideas and Terms 333 Chapter 4 Chapter Review 337 Chapter 4 Chapter Test 344 Chapters 1-4 Cumulative Review 347 5.1 Exponents 354 5.2 Exponents and Scientific Notation 367 5.3 Introduction to Polynomials 380 5.4 Addition and Subtraction with Polynomials 387 5.5 Multiplication with Polynomials 394 5.6 Special Products of Binomials 400 5.7 Division with Polynomials 408 Chapter 5 Index of Key Ideas and Terms 416 Chapter 5 Chapter Review 419 Chapter 5 Chapter Test 423 Chapters 1-5 Cumulative Review 425 Chapter 3 Formulas and Linear Inequalities 177 Chapter 4 Linear Equations and Functions 255 Chapter 5 Exponents and Polynomials 353 Table of Contents.indd 610/8/2010 2:51:25 PMvii TABLE OF CONTENTS 6.1 Greatest Common Factor and Factoring by Grouping 430 6.2 Factoring Trinomials: x 2 + bx + c 441 6.3 Factoring Trinomials: ax 2 + bx + c 448 6.4 Special Factoring Techniques 459 6.5 Additional Factoring Practice 468 6.6 Solving Quadratic Equations by Factoring 471 6.7 Applications of Quadratic Equations 481 Chapter 6 Index of Key Ideas and Terms 492 Chapter 6 Chapter Review 497 Chapter 6 Chapter Test 501 Chapters 1-6 Cumulative Review 502 7.1 Multiplication and Division with Rational Expressions 508 7.2 Addition and Subtraction with Rational Expressions 519 7.3 Complex Fractions 529 7.4 Solving Equations with Rational Expressions 536 7.5 Applications 549 7.6 Variation 560 Chapter 7 Index of Key Ideas and Terms 572 Chapter 7 Chapter Review 576 Chapter 7 Chapter Test 581 Chapters 1-7 Cumulative Review 583 8.1 Systems of Linear Equations: Solutions by Graphing 588 8.2 Systems of Linear Equations: Solutions by Substitution 599 8.3 Systems of Linear Equations: Solutions by Addition 606 8.4 Applications: Distance-Rate-Time, Number Problems, Amounts and Costs 614 8.5 Applications: Interest and Mixture 626 8.6 Systems of Linear Equations: Three Variables 634 8.7 Matrices and Gaussian Elimination 646 8.8 Graphing Systems of Linear Inequalities 659 Chapter 8 Index of Key Ideas and Terms 665 Chapter 8 Chapter Review 670 Chapter 8 Chapter Test 675 Chapters 1-8 Cumulative Review 677 Chapter 6 Factoring Polynomials and Solving Quadratic Equations 429 Chapter 7 Rational Expressions 507 Chapter 8 Systems of Linear Equations 587 Table of Contents.indd 710/8/2010 2:51:26 PMviii TABLE OF CONTENTS 9.1 Roots and Radicals 682 9.2 Simplifying Radicals 690 9.3 Rational Exponents 698 9.4 Operations with Radicals 708 9.5 Equations with Radicals 719 9.6 Functions with Radicals 726 9.7 Introduction to Complex Numbers 736 9.8 Multiplication and Division with Complex Numbers 743 Chapter 9 Index of Key Ideas and Terms 750 Chapter 9 Chapter Review 756 Chapter 9 Chapter Test 760 Chapters 1-9 Cumulative Review 762 10.1 Solving Quadratic Equations 768 10.2 The Quadratic Formula: x bbac a = −±− 24 2 780 10.3 Applications 789 10.4 Equations in Quadratic Form 799 10.5 Graphing Quadratic Functions: Parabolas 806 10.6 Solving Quadratic and Rational Inequalities 824 Chapter 10 Index of Key Ideas and Terms 840 Chapter 10 Chapter Review 844 Chapter 10 Chapter Test 849 Chapters 1-10 Cumulative Review 851 11.1 Algebra of Functions 856 11.2 Composition of Functions and Inverse Functions 869 11.3 Exponential Functions 886 11.4 Logarithmic Functions 900 11.5 Properties of Logarithms 907 11.6 Common Logarithms and Natural Logarithms 917 11.7 Logarithmic and Exponential Equations and Change-of-Base 925 11.8 Applications 934 Chapter 11 Index of Key Ideas and Terms 941 Chapter 11 Chapter Review 946 Chapter 11 Chapter Test 952 Chapters 1-11 Cumulative Review 955 Chapter 9 Roots, Radicals, and Complex Numbers 681 Chapter 10 Quadratic Equations 767 Chapter 11 Exponential and Logarithmic Functions 855 Table of Contents.indd 810/8/2010 2:51:26 PMix TABLE OF CONTENTS 12.1 Translations and Reflections 962 12.2 Parabolas as Conic Sections 976 12.3 Distance Formula and Circles 985 12.4 Ellipses and Hyperbolas 996 12.5 Nonlinear Systems of Equations 1009 Chapter 12 Index of Key Ideas and Terms 1016 Chapter 12 Chapter Review 1021 Chapter 12 Chapter Test 1024 Chapters 1-12 Cumulative Review 1026 13.1 Sequences 1032 13.2 Sigma Notation 1040 13.3 Arithmetic Sequences 1046 13.4 Geometric Sequences and Series 1057 13.5 The Binomial Theorem 1069 Chapter 13 Index of Key Ideas and Terms 1078 Chapter 13 Chapter Review 1082 Chapter 13 Chapter Test 1086 Chapters 1-13 Cumulative Review 1088 A.1 Decimals and Percents 1091 A.2 Synthetic Division and the Remainder Theorem 1103 A.3 Using a Graphing Calculator to Solve Equations 1109 A.4 Determinants 1115 A.5 Cramer’s Rule 1124 A.6 Powers, Roots, and Prime Factorizations 1131 Answers 1135 Index 1207 Chapter 12 Conic Sections 961 Chapter 13 Sequences, Series, and the Binomial Theorem 1031 Appendix Table of Contents.indd 910/8/2010 2:51:27 PMNext >