# Beginning Algebra

**by**Miller, Julie; O'Neill, Molly; Hyde, Nancy

### 9780073384481

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## Summary

## Table of Contents

# Beginning Algebra, Miller, O'Neill, Hyde, 4 edition

### Chapter 1: The Set of Real Numbers

#### 1.1 Fractions

#### 1.2 Introduction to Algebra and the Set of Real Numbers

#### 1.3 Exponents, Square Roots, and the Order of Operations

#### 1.4 Addition of Real Numbers

#### 1.5 Subtraction of Real Numbers

Problem Recognition Exercises—Addition and Subtraction of Real Numbers

#### 1.6 Multiplication and Division of Real Numbers

Problem Recognition Exercises—Adding, Subtracting, Multiplying, and Dividing Real Numbers

#### 1.7 Properties of Real Numbers and Simplifying Expressions

### Chapter 2: Linear Equations and Inequalities

#### 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality

#### 2.2 Solving Linear Equations

#### 2.3 Linear Equations: Clearing Fractions and Decimals

Problem Recognition Exercises—Equations vs.Expressions

#### 2.4 Applications of Linear Equations: Introduction to Problem Solving

#### 2.5 Applications Involving Percents

#### 2.6 Formulas and Applications of Geometry

#### 2.7 Mixture Applications and Uniform Motion

#### 2.8 Linear Inequalities

### Chapter 3: Graphing Linear Equations in Two Variables

#### 3.1 Rectangular Coordinate System

#### 3.2 Linear Equations in Two Variables

#### 3.3 Slope of a Line and Rate of Change

#### 3.4 Slope-Intercept Form of a Linear Equation

Problem Recognition Exercises—Linear Equations in Two Variables

#### 3.5 Point-Slope Formula

#### 3.6 Applications of Linear Equations and Modeling

### Chapter 4: Systems of Linear Equations in Two Variables

#### 4.1 Solving Systems of Equations by the Graphing Method

#### 4.2 Solving Systems of Equations by the Substitution Method

#### 4.3 Solving Systems of Equations by the Addition Method

Problem Recognition Exercises—Systems of Equations

#### 4.4 Applications of Linear Equations in Two Variables

#### 4.5 Linear Inequalities and Systems of Inequalities in Two Variables

### Chapter 5: Polynomials and Properties of Exponents

#### 5.1 Multiplying and Dividing Expressions with Common Bases

#### 5.2 More Properties of Exponents

#### 5.3 Definitions of and Problem Recognition Exercises—Properties of Exponents

#### 5.4 Scientific Notation

#### 5.5 Addition and Subtraction of Polynomials

#### 5.6 Multiplication of Polynomials and Special Products

#### 5.7 Division of Polynomials

Problem Recognition Exercises—Operations on Polynomials

### Chapter 6: Factoring Polynomials

#### 6.1 Greatest Common Factor and Factoring by Grouping

#### 6.2 Factoring Trinomials of the Form x^2 + bx + c

#### 6.3 Factoring Trinomials: Trial-and-Error Method

#### 6.4 Factoring Trinomials: AC-Method

#### 6.5 Difference of Squares and Perfect Square Trinomials

#### 6.6 Sum and Difference of Cubes

Problem Recognition Exercises—Factoring Strategy

#### 6.7 Solving Equations Using the Zero Product Rule

Problem Recognition Exercises— Polynomial Expressions versus Polynomial Equations

#### 6.8 Applications of Quadratic Equations

### Chapter 7: Rational Expressions and Equations

#### 7.1 Introduction to Rational Expressions

#### 7.2 Multiplication and Division of Rational Expressions

#### 7.3 Least Common Denominator

#### 7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises—Operations on Rational Expressions

#### 7.5 Complex Fractions

#### 7.6 Rational Equations

Problem Recognition Exercises—Comparing Rational Equations and Rational Expressions

#### 7.7 Applications of Rational Equations and Proportions

#### 7.8 Variation

### Chapter 8: Radicals

#### 8.1 Introduction to Roots and Radicals

#### 8.2 Simplifying Radicals

#### 8.3 Addition and Subtraction of Radicals

#### 8.4 Multiplication of Radicals

#### 8.5 Division of Radicals and Rationalization

Problem Recognition Exercises—Operations on Radicals

#### 8.6 Radical Equations

#### 8.7 Rational Exponents

### Chapter 9: Quadratic Equations, Complex Numbers, and Functions

#### 9.1 The Square Root Property

#### 9.2 Completing the Square

#### 9.3 Quadratic Formula

Problem Recognition Exercises—Solving Different Types of Equations