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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
vii
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
viii Contents
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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
Contents ix
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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
Contents xi
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