Preface 

viii  

Operations on Real Numbers and Algebraic Expressions 


1  (73) 


2  (6) 

The Number Systems and the Real Number Line 


8  (10) 

Adding, Subtracting, Multiplying, and Dividing Integers 


18  (10) 

Adding, Subtracting, Multiplying, and Dividing Rational Numbers Expressed as Fractions and Decimals 


28  (13) 

Putting the Concepts Together (Sections 1.21.4) 


40  (1) 

Properties of Real Numbers 


41  (8) 

Exponents and the Order of Operations 


49  (8) 

Simplifying Algebraic Expressions 


57  (17) 

Chapter 1 Activity: The Math Game 


65  (1) 


66  (7) 


73  (1) 

Equations and Inequalities in One Variable 


74  (100) 

Linear Equations: The Addition and Multiplication Properties of Equality 


75  (9) 

Linear Equations: Using the Properties Together 


84  (9) 

Solving Linear Equations Involving Fractions and Decimals; Classifying Equations 


93  (10) 

Evaluating Formulas and Solving Formulas for a Variable 


103  (14) 

Putting the Concepts Together (Sections 2.12.4) 


116  (1) 

Introduction to Problem Solving: Direct Translation Problems 


117  (14) 

Problem Solving: Direct Translation Problems Involving Percent 


131  (8) 

Problem Solving: Geometry and Uniform Motion 


139  (11) 

Solving Linear Inequalities in One Variable 


150  (24) 

Chapter 2 Activity: Pass to the Right 


164  (1) 


165  (7) 


172  (2) 

Introduction to Graphing and Equations of Lines 


174  (98) 

The Rectangular Coordinate System and Equations in Two Variables 


175  (16) 

Graphing Equations in Two Variables 


191  (15) 


206  (11) 

SlopeIntercept Form of a Line 


217  (10) 

PointSlope Form of a Line 


227  (8) 

Parallel and Perpendicular Lines 


235  (10) 

Putting the Concepts Together (Sections 3.13.6) 


244  (1) 


245  (7) 

Linear Inequalities in Two Variables 


252  (20) 

Chapter 3 Activity: Graphing Practice 


261  (1) 


262  (8) 


270  (1) 

Cumulative Review Chapters 13 


271  (1) 

Systems of Linear Equations and Inequalities 


272  (71) 

Solving Systems of Linear Equations by Graphing 


273  (12) 

Solving Systems of Linear Equations Using Substitution 


285  (11) 

Solving Systems of Linear Equations Using Elimination 


296  (11) 

Putting the Concepts Together (Sections 4.14.3) 


306  (1) 

Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations 


307  (7) 

Solving Mixture Problems Using Systems of Linear Equations 


314  (12) 

Systems of Linear Inequalities 


326  (17) 

Chapter 4 Activity: Find the Numbers 


334  (1) 


334  (7) 


341  (2) 

Exponents and Polynomials 


343  (64) 

Adding and Subtracting Polynomials 


344  (10) 

Multiplying Monomials: The Product and Power Rules 


354  (6) 


360  (11) 

Dividing Monomials: The Quotient Rule and Integer Exponents 


371  (12) 

Putting the Concepts Together (Sections 5.15.4) 


383  (1) 


383  (8) 

Applying Exponent Rules: Scientific Notation 


391  (16) 

Chapter 5 Activity: What Is the Question? 


398  (2) 


400  (4) 


404  (1) 

Cumulative Review Chapters 15 


405  (2) 


407  (67) 

Greatest Common Factor and Factoring by Grouping 


408  (10) 

Factoring Trinomials of the Form x2 + bx + c 


418  (9) 

Factoring Trinomials of the Form ax2 + bx + c, a 1 


427  (9) 

Factoring Special Products 


436  (8) 

Summary of Factoring Techniques 


444  (7) 

Putting the Concepts Together (Sections 6.16.5) 


450  (1) 

Solving Polynomial Equations by Factoring 


451  (9) 

Modeling and Solving Problems with Quadratic Equations 


460  (14) 

Chapter 6 Activity: Which One Does Not Belong? 


468  (1) 


469  (4) 


473  (1) 

Getting Ready for Intermediate Algebra: A Review of Chapters 16 


474  (89) 

Rational Expressions and Equations 


476  (87) 

Simplifying Rational Expressions 


477  (8) 

Multiplying and Dividing Rational Expressions 


485  (9) 

Adding and Subtracting Rational Expressions with a Common Denominator 


494  (7) 

Finding the Least Common Denominator and Forming Equivalent Rational Expressions 


501  (8) 

Adding and Subtracting Rational Expressions with Unlike Denominators 


509  (11) 

Complex Rational Expressions 


520  (9) 

Putting the Concepts Together (Sections 7.17.6) 


528  (1) 


529  (12) 

Models Involving Rational Equations 


541  (22) 

Chapter 7 Activity: Correct the Quiz 


555  (1) 


556  (5) 


561  (2) 

Getting Ready for Intermediate Algebra: A Review of Chapters 17 


563  

Graphs, Relations, and Functions 


565  (94) 


566  (11) 


577  (7) 

Putting the Concepts Together (Sections 8.18.2) 


584  (1) 

An Introduction to Functions 


584  (13) 

Functions and Their Graphs 


597  (10) 


607  (14) 


621  (11) 

Absolute Value Equations and Inequalities 


632  (27) 

Chapter 8 Activity: Shifting Discovery 


644  (1) 


644  (12) 


656  (3) 

Radicals and Rational Exponents 


659  (84) 


660  (6) 

nth Roots and Rational Exponents 


666  (8) 

Simplify Expressions Using the Laws of Exponents 


674  (6) 

Simplifying Radical Expressions 


680  (12) 

Adding, Subtracting, and Multiplying Radical Expressions 


692  (7) 

Rationalizing Radical Expressions 


699  (6) 

Putting the Concepts Together (Sections 9.19.6) 


705  (1) 

Functions Involving Radicals 


705  (7) 

Radical Equations and Their Applications 


712  (10) 

The Complex Number System 


722  (21) 

Chapter 9 Activity: Which One Does Not Belong? 


733  (1) 


734  


714  (27) 

Cumulative Review Chapters 19 


741  (2) 

Quadratic Equations and Functions 


743  (94) 

Solving Quadratic Equations by Completing the Square 


744  (13) 

Solving Quadratic Equations by the Quadratic Formula 


757  (15) 

Solving Equations Quadratic in Form 


772  (9) 

Putting the Concepts Together (Sections 10.110.3) 


780  (1) 

Graphing Quadratic Functions Using Transformations 


781  (14) 

Graphing Quadratic Functions Using Properties 


795  (16) 


811  (10) 


821  (16) 

Chapter 10 Activity: Presidential Decision Making 


827  (1) 


828  (7) 


835  (2) 

Exponential and Logarithmic Functions 


837  (75) 

Composite Functions and Inverse Functions 


838  (14) 


852  (18) 


870  (14) 

Putting the Concepts Together (Sections 11.111.3) 


883  (1) 


884  (10) 

Exponential and Logarithmic Equations 


894  (18) 

Chapter 11 Activity: Correct the Quiz 


903  (1) 


904  (5) 


909  (1) 

Cumulative Review Chapters 111 


910  (2) 


912  (61) 

Distance and Midpoint Formulas 


913  (7) 


920  (7) 


927  (11) 


938  (11) 


949  (9) 

Putting the Concepts Together (Sections 12.112.5) 


957  (1) 

Nonlinear Systems of Equations 


958  (15) 

Chapter 12 Activity: How Do You Know That . . . ? 


966  (1) 


966  (6) 


972  (1) 

Sequences, Series, and the Binomial Theorem 


973  


974  (8) 


982  (8) 

Geometric Sequences and Series 


990  (12) 

Putting the Concepts Together (Sections 13.113.3) 


1001  (1) 


1002  

Chapter 13 Activity: Pass to the Right 


1008  (1) 


1008  (4) 


1012  (1) 

Cumulative Review Chapters 113 


1013  
Appendix A: Fractions, Decimals, and Percents 

1  (1) 
Appendix B: Synthetic Division 

1  (1) 
Appendix C: Geometry Review 

1  (1) 
Appendix D: The Library of Functions 

1  (1) 
Appendix E: More on Systems of Linear Equations 

1  (1) 
Appendix F: Table of Square Roots 

1  (1) 
Answers to Quick Check Exercises 

1  (1) 
Answers to Selected Exercises 

1  (1) 
Applications Index 

1  (1) 
Subject Index 

1  (1) 
Photo Credits 

1  