Beginningand Intermediate AlgebraAn Integrated Approach

6th Edition

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

R. David GustafsonRock Valley College

Rosemary M. KarrCollin College

Marilyn B. MasseyCollin College

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Chapter 1 Real Numbers and Their Basic Properties 1

1.1 Real Numbers and Their Graphs 21.2 Fractions 131.3 Exponents and Order of Operations 301.4 Adding and Subtracting Real Numbers 411.5 Multiplying and Dividing Real Numbers 501.6 Algebraic Expressions 581.7 Properties of Real Numbers 66

� PROJECTS 74

CHAPTER REVIEW 75

CHAPTER 1 TEST 82

Chapter 2 Equations and Inequalities 83

2.1 Solving Basic Linear Equations in One Variable 842.2 Solving More Linear Equations in One Variable 98 2.3 Simplifying Expressions to Solve Linear Equations in One Variable 1072.4 Formulas 1152.5 Introduction to Problem Solving 1222.6 Motion and Mixture Problems 1312.7 Solving Linear Inequalities in One Variable 139

� PROJECTS 148

CHAPTER REVIEW 148

CHAPTER 2 TEST 154

CUMULATIVE REVIEW EXERCISES 155

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Contents

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Chapter 3 Graphing and Solving Systems of Linear Equations and Linear Inequalities 157

3.1 The Rectangular Coordinate System 1583.2 Graphing Linear Equations 1693.3 Solving Systems of Linear Equations by Graphing 1843.4 Solving Systems of Linear Equations by Substitution 1963.5 Solving Systems of Linear Equations by Elimination (Addition) 2023.6 Solving Applications of Systems of Linear Equations 2103.7 Solving Systems of Linear Inequalities 221

� PROJECTS 235

CHAPTER REVIEW 236

CHAPTER 3 TEST 243

Chapter 4 Polynomials 245

4.1 Natural-Number Exponents 2464.2 Zero and Negative-Integer Exponents 2544.3 Scientific Notation 2614.4 Polynomials and Polynomial Functions 2684.5 Adding and Subtracting Polynomials 2794.6 Multiplying Polynomials 2874.7 Dividing Polynomials by Monomials 2974.8 Dividing Polynomials by Polynomials 303

� PROJECTS 311

CHAPTER REVIEW 311

CHAPTER 4 TEST 316

CUMULATIVE REVIEW EXERCISES 317

Chapter 5 Factoring Polynomials 319

5.1 Factoring Out the Greatest Common Factor; Factoring by Grouping 3205.2 Factoring the Difference of Two Squares 3295.3 Factoring Trinomials with a Leading Coefficient of 1 3355.4 Factoring General Trinomials 3455.5 Factoring the Sum and Difference of Two Cubes 3545.6 Summary of Factoring Techniques 3595.7 Solving Equations by Factoring 3635.8 Problem Solving 369

� PROJECTS 376

CHAPTER REVIEW 377

CHAPTER 5 TEST 381

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Chapter 6 Rational Expressions and Equations; Ratio and Proportion 382

6.1 Simplifying Rational Expressions 3836.2 Multiplying and Dividing Rational Expressions 3926.3 Adding and Subtracting Rational Expressions 4026.4 Simplifying Complex Fractions 4146.5 Solving Equations That Contain Rational Expressions 4216.6 Solving Applications of Equations That Contain Rational Expressions 4286.7 Ratios 4346.8 Proportions and Similar Triangles 440

� PROJECTS 452

CHAPTER REVIEW 452

CHAPTER 6 TEST 459

CUMULATIVE REVIEW EXERCISES 460

Chapter 7 More Equations, Inequalities, and Factoring 461

7.1 Review of Solving Linear Equations and Inequalities in One Variable 4627.2 Solving Equations in One Variable Containing Absolute Values 4757.3 Solving Inequalities in One Variable Containing an Absolute-Value Term 4817.4 Review of Factoring 4887.5 Review of Rational Expressions 5017.6 Synthetic Division 514

� PROJECTS 521

CHAPTER REVIEW 523

CHAPTER 7 TEST 531

Chapter 8 Writing Equations of Lines, Functions, and Variation 532

8.1 A Review of the Rectangular Coordinate System 5338.2 Slope of a Line 5428.3 Writing Equations of Lines 5548.4 A Review of Functions 5678.5 Graphs of Nonlinear Functions 5778.6 Variation 591

� PROJECTS 600

CHAPTER REVIEW 601

CHAPTER 8 TEST 608

CUMULATIVE REVIEW EXERCISES 609

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Chapter 9 Radicals and Rational Exponents 610

9.1 Radical Expressions 6119.2 Applications of the Pythagorean Theorem and the Distance Formula 6249.3 Rational Exponents 6319.4 Simplifying and Combining Radical Expressions 6409.5 Multiplying and Dividing Radical Expressions 6519.6 Radical Equations 6619.7 Complex Numbers 670

� PROJECTS 680

CHAPTER REVIEW 681

CHAPTER 9 TEST 689

Chapter 10 Quadratic Functions, Inequalities, and Algebra of Functions 691

10.1 Solving Quadratic Equations Using the Square-Root Property and by Completingthe Square 692

10.2 Solving Quadratic Equations by the Quadratic Formula 70310.3 The Discriminant and Equations That Can Be Written in Quadratic Form 71110.4 Graphs of Quadratic Functions 72010.5 Quadratic and Other Nonlinear Inequalities 73510.6 Algebra and Composition of Functions 74610.7 Inverses of Functions 753

� PROJECTS 763

CHAPTER REVIEW 764

CHAPTER 10 TEST 772

CUMULATIVE REVIEW EXERCISES 773

Chapter 11 Exponential and Logarithmic Functions 775

11.1 Exponential Functions 77611.2 Base-e Exponential Functions 78811.3 Logarithmic Functions 79611.4 Natural Logarithms 80711.5 Properties of Logarithms 81311.6 Exponential and Logarithmic Equations 823

� PROJECTS 835

CHAPTER REVIEW 836

CHAPTER 11 TEST 842

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Chapter 12 Conic Sections and More Graphing 843

12.1 The Circle and the Parabola 84412.2 The Ellipse 85712.3 The Hyperbola 86912.4 Piecewise-Defined Functions and the Greatest Integer Function 879

� PROJECTS 886

CHAPTER REVIEW 886

CHAPTER 12 TEST 892

CUMULATIVE REVIEW EXERCISES 893

Chapter 13 More Systems of Equations and Inequalities 895

13.1 Solving Systems of Two Linear Equations or Inequalities in Two Variables 89613.2 Solving Systems of Three Linear Equations in Three Variables 90913.3 Solving Systems of Linear Equations Using Matrices 91913.4 Solving Systems of Linear Equations Using Determinants 92813.5 Solving Systems of Equations and Inequalities Containing One or More

Second-Degree Terms 939� PROJECTS 946

CHAPTER REVIEW 948

CHAPTER 13 TEST 955

Chapter 14 Miscellaneous Topics 957

14.1 The Binomial Theorem 95814.2 The nth Term of a Binomial Expansion 96514.3 Arithmetic Sequences 96814.4 Geometric Sequences 97714.5 Infinite Geometric Sequences 98514.6 Permutations and Combinations 98914.7 Probability 1000

� PROJECTS 1006

CHAPTER REVIEW 1007

CHAPTER 14 TEST 1012

CUMULATIVE REVIEW EXERCISES 1013

Glossary G-1

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Appendix I Symmetries of Graphs A-1

Appendix II Tables A-7

Table A Powers and Roots A-7Table B Base-10 Logarithms A-8Table C Base-e Logarithms A-9

Appendix III Answers to Selected Exercises A-11

Index I-1

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