TheAngel author teammeets the needs of todayrs"s learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process. For all readers interested in algebra.

Preface

To the Student

**1. Real Numbers**

1.1 Study Skills for Success in Mathematics

1.2 Problem Solving

1.3 Fractions

1.4 The Real Number System

1.5 Inequalities

Mid-Chapter Test: Sections 1.1—1.5

1.6 Addition of Real Numbers

1.7 Subtraction of Real Numbers

1.8 Multiplication and Division of Real Numbers

1.9 Exponents, Parentheses, and the Order of Operations

1.10 Properties of the Real Number System

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Practice Test

**2. Solving Linear Equations**

2.1 Combining Like Terms

2.2 The Addition Property of Equality

2.3 The Multiplication Property of Equality

2.4 Solving Linear Equations with a Variable on Only One Side of the Equation

Mid-Chapter Test: Sections 2.1—2.4

2.5 Solving Linear Equations with the Variable on Both Sides of the Equation

2.6 Formulas

2.7 Ratios and Proportions

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Practice Test

Cumulative Review Test

**3. Applications of Algebra**

3.1 Changing Application Problems into Equations

3.2 Solving Application Problems

Mid-Chapter Test: Sections 3.1—3.2

3.3 Geometric Problems

3.4 Motion, Money, and Mixture Problems

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Practice Test

Cumulative Review Test

**4. Graphing Linear Equations**

4.1 The Cartesian Coordinate System and Linear Equations in Two Variables

4.2 Graphing Linear Equations

4.3 Slope of a Line

Mid-Chapter Test: Sections 4.1—4.3

4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Practice Test

Cumulative Review Test

**5. Exponents and Polynomials**

5.1 Exponents

5.2 Negative Exponents

5.3 Scientific Notation

Mid-Chapter Test: Sections 5.1—5.3

5.4 Addition and Subtraction of Polynomials

5.5 Multiplication of Polynomials

5.6 Division of Polynomials

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Practice Test

Cumulative Review Test

**6. Factoring**

6.1 Factoring a Monomial from a Polynomial

6.2 Factoring by Grouping

6.3 Factoring Trinomials of the Form *ax* ^{2} + *bx* + *c*, *a* = 1

6.4 Factoring Trinomials of the Form *ax* ^{2} + *bx* + *c*, *a* ≠ 1

Mid-Chapter Test: Sections 6.1—6.4

6.5 Special Factoring Formulas and a General Review of Factoring

6.6 Solving Quadratic Equations Using Factoring

6.7 Applications of Quadratic Equations

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Practice Test

Cumulative Review Test

**7. Rational Expressions and Equations**

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator

7.4 Addition and Subtraction of Rational Expressions

Mid-Chapter Test: Sections 7.1—7.4

7.5 Complex Fractions

7.6 Solving Rational Equations

7.7 Rational Equations: Applications and Problem Solving

7.8 Variation

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Practice Test

Cumulative Review Test

**8. Functions and Their Graphs**

8.1 More on Graphs

8.2 Functions

8.3 Linear Functions

Mid-Chapter Test: Sections 8.1—8.3

8.4 Slope, Modeling, and Linear Relationships

8.5 The Algebra of Functions

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Practice Test

Cumulative Review Test

**9. Systems of Linear Equations**

9.1 Solving Systems of Equations Graphically

9.2 Solving Systems of Equations by Substitution

9.3 Solving Systems of Equations by the Addition Method

9.4 Solving Systems of Linear Equations in Three Variables

Mid-Chapter Test: Sections 9.1—9.4

9.5 Systems of Linear Equations: Applications and Problem Solving

9.6 Solving Systems of Equations Using Matrices

9.7 Solving Systems of Equations Using Determinants and Cramer’s Rule

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Practice Test

Cumulative Review Test

**10. Inequalities in One and Two Variables**

10.1 Solving Linear Inequalities in One Variable

10.2 Solving Equations and Inequalities Containing Absolute Values

Mid-Chapter Test: Sections 10.1—10.2

10.3 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Practice Test

Cumulative Review Test

**11. Roots, Radicals, and Complex Numbers**

11.1 Roots and Radicals

11.2 Rational Exponents

11.3 Simplifying Radicals

11.4 Adding, Subtracting, and Multiplying Radicals

Mid-Chapter Test: Sections 11.1—11.4

11.5 Dividing Radicals

11.6 Solving Radical Equations

11.7 Complex Numbers

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Practice Test

Cumulative Review Test

**12. Quadratic Functions**

12.1 Solving Quadratic Equations by Completing the Square

12.2 Solving Quadratic Equations by the Quadratic Formula

12.3 Quadratic Equations: Applications and Problem Solving

Mid-Chapter Test: Sections 12.1—12.3

12.4 Factoring Expressions and Solving Equations That Are Quadratic in Form

12.5 Graphing Quadratic Functions

12.6 Quadratic and Other Inequalities in One Variable

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Practice Test

Cumulative Review Test

**13. Exponential and Logarithmic Functions**

13.1 Composite and Inverse Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

Mid-Chapter Test: Sections 13.1—13.4

13.5 Common Logarithms

13.6 Exponential and Logarithmic Equations

13.7 Natural Exponential and Natural Logarithmic Functions 818

Chapter 13 Summary 829

Chapter 13 Review Exercises 832

Chapter 13 Practice Test 835

Cumulative Review Test 836

**14. Conic Sections**

14.1 The Parabola and the Circle

14.2 The Ellipse

Mid-Chapter Test: Sections 14.1—14.2

14.3 The Hyperbola

14.4 Nonlinear Systems of Equations and Their Applications

Chapter 14 Summary

Chapter 14 Review Exercises

Chapter 14 Practice Test

Cumulative Review Test

**15. Sequences, Series, and the Binomial Theorem**

15.1 Sequences and Series

15.2 Arithmetic Sequences and Series

15.3 Geometric Sequences and Series

Mid-Chapter Test: Sections 15.1—15.3

15.4 The Binomial Theorem

Chapter 15 Summary

Chapter 15 Review Exercises

Chapter 15 Practice Test

Cumulative Review Test

**Appendices**

A. Review of Decimals and Percent

B. Finding the Greatest Common Factor and Least Common Denominator

C. Geometry

D. Review of Exponents, Polynomials, and Factoring

Answers

Applications Index

Subject Index