Homework Helpers: Algebra Book

Preface 11

Capter 1 Numbers 13

Lesson 1-1 Types of Numbers 14

Lesson 1-2 Operations and Symbols 19

Lesson 1-3 Properties of Real Numbers 20

Lesson 1-4 Properties of Zero and One 23

Lesson 1-5 Absolute Value 26

Lesson 1-6 Manipulating Rational Numbers 27

Lesson 1-7 The Order of Operations 34

Lesson 1-8 The Distributive Property 35

Lesson 1-9 Evaluating Expressions 37

Chapter 2 Exponents 41

Lesson 2-1 Positive Integer Powers 41

Lesson 2-2 Rules for Exponents 45

Lesson 2-3 Negative Integer Powers 49

Lesson 2-4 Zero as an Exponent 51

Lesson 2-5 Powers of Quotients and Products 52

Lesson 2-6 Scientific Notation 54

Chapter 3 Equations and Equality 59

Lesson 3-1 Equations 59

Lesson 3-2 Equality 60

Lesson 3-3 Algebraic Properties of Equality 62

Lesson 3-4 Solving Linear Equations in One Step 63

Lesson 3-5 Solving Linear Equations Using Several Steps 68

Lesson 3-6 Equations Involving Absolute Value 74

Chapter 4 Inequalities and Graphs 81

Lesson 4-1 Properties of Inequalities 83

Lesson 4-2 Solving Inequalities in One Step 84

Lesson 4-3 Solving Inequalities Using Several Steps 88

Lesson 4-4 Graphing Inequalities Using the Number Line 90

Lesson 4-5 Graphing Compound Inequalities 95

Lesson 4-6 Inequalities and Absolute Value 97

Chapter 5 Relations, Functions, and Graphs 105

Lesson 5-1 Relations 105

Lesson 5-2 Functions 107

Lesson 5-3 Formulas 108

Lesson 5-4 Tables 109

Lesson 5-5 The Cartesian Coordinate System 110

Lesson 5-6 Graphs of Functions and Relations 114

Chapter 6 Linear Equations 121

Lesson 6-1 Linear Functions and Calculating Slopes 121

Lesson 6-2 Intercepts 127

Lesson 6-3 Point-Slope Form 129

Lesson 6-4 Slope-Intercept Form 130

Lesson 6-5 Standard Form 132

Lesson 6-6 Horizontal and Vertical Lines 135

Lesson 6-7 Graphing Linear Equations 138

Chapter 7 Systems of Linear Equations 147

Lesson 7-1 The Graphical Method 148

Lesson 7-2 The Substitution/Elimination Method 150

Lesson 7-3 The Addition/Subtraction Method 153

Chapter 8 Monomials and Polynomials 161

Lesson 8-1 Terminology 161

Lesson 8-2 Adding and Subtracting Monomials 163

Lesson 8-3 Multiplying and Dividing Monomials 164

Lesson 8-4 Monomials as the Base of an Exponential Expression 167

Lesson 8-5 Adding and Subtracting Polynomials 168

Lesson 8-6 Multiplying Polynomials 170

Lesson 8-7 Special Products 173

Lesson 8-8 Dividing Polynomials by Monomials 176

Lesson 8-9 Factoring Techniques 177

Lesson 8-10 Solving Factored Equations 180

Chapter 9 Quadratic Equations 185

Lesson 9-1 Square Roots 185

Lesson 9-2 The Difference Between Two Squares 188

Lesson 9-3 Factoring Quadratic Expressions of the Form X² + bx + c 193

Lesson 9-4 Factoring Quadratic Expressions in General 197

Lesson 9-5 Solving Quadratic Equations by Factoring 200

Lesson 9-6 Solving Quadratic Equations by Completing the Square 202

Lesson 9-7 Solving Quadratic Equations Using the Quadratic Formula 206

Chapter 10 Rational Expressions 213

Lesson 10-1 Simplifying Rational Expressions 213

Lesson 10-2 Multiplying Rational Expressions 216

Lesson 10-3 Dividing Rational Expressions 217

Lesson 10-4 Adding and Subtracting Rational Expressions 219

Chapter 11 Applications 225

Lesson 11-1 How to Approach Word Problems 225

Lesson 11-2 Rates and Percentages 227

Lesson 11-3 Finding Integers 229

Lesson 11-4 Rate, Time, and Distance Problems 232

Lesson 11-5 Money Problems 234

Lesson 11-6 Mixture Problems 236

Final Exam 241

Index 251

About the Author 255