# algebra success in 20 minutes a day

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ALGEBRA SUCCESSIN 20 MINUTES A DAY

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ALGEBRA SUCCESSIN 20 MINUTES A DAY

4th Edition

NEW

YORK

Copyright 2010 LearningExpress, LLC. All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by LearningExpress, LLC, New York. Library of Congress Cataloging-in-Publication Data: Algebra success in 20 minutes a day.4th ed. p.cm. ISBN: 978-1-57685-719-9 1. AlgebraStudy and teaching. I. LearningExpress (Organization). II. Title: Algebra success in twenty minutes a day. QA159.J59 2010 512dc22 2009035551 Printed in the United States of America 987654321 Fourth Edition ISBN: 978-1-57685-719-9 For more information or to place an order, contact LearningExpress at: LearningExpress 2 Rector Street 26th Floor New York, NY 10006 Or visit us at: www.learnatest.com

ContentsIntroduction Pretest LESSON 1Overcoming Math Anxiety How to Use This Book Make a CommitmentWORKING WITH INTEGERS What Is an Integer? Adding and Subtracting Integers Multiplying and Dividing Integers WORKING WITH ALGEBRAIC EXPRESSIONS Simplifying Expressions Evaluating Algebraic Expressions COMBINING LIKE TERMS What Are Like Terms? Using the Distributive Property to Combine Like Terms SOLVING BASIC EQUATIONS What Is an Equation? Solving Equations Using Addition or Subtraction Checking Your Answers Solving Equations Using Multiplication or Division Setting Up Equations for Word Problems SOLVING MULTISTEP EQUATIONS Solving Equations Requiring More Than One Step Solving Equations That Have a Fraction in Front of the Variablev

ix x xi 1 13

LESSON 2

21

LESSON 3

27

LESSON 4

31

LESSON 5

39

LESSON 6

SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES OF THE EQUATION What to Do When You Have Variables on Both Sides of the Equation Using the Distributive Property Solving More Complex Equations Equations without a Variable in the Answer USING FORMULAS TO SOLVE EQUATIONS GRAPHING LINEAR EQUATIONS What Is a Graph? Plotting Points on a Graph Using the Slope and Y-Intercept Graphing Linear Equations Using Slope and Y-Intercept SOLVING INEQUALITIES What Is an Inequality? Solving Inequalities Checking Your Answers GRAPHING INEQUALITIES What Is a Number Line? Graphing Linear Inequalities Special Cases of Inequalities GRAPHING SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES What Is a Linear Equation? What Is a System of Linear Equations? Solving Systems of Inequalities Graphically SOLVING SYSTEMS OF EQUATIONS ALGEBRAICALLY How to Use the Elimination Method How to Use the Substitution Method WORKING WITH EXPONENTS What Is an Exponent? Adding and Subtracting with Exponents Multiplying with Exponents Dividing with Exponents What to Do with Exponents When You Raise a Quantity to a Power MULTIPLYING POLYNOMIALS What Is a Polynomial? Multiplying a Polynomial by a Monomial Multiplying a Binomial by a Binomial Multiplying a Binomial by a Trinomial

45

LESSON 7 LESSON 8

51 57

LESSON 9

67

LESSON 10

73

LESSON 11

83

LESSON 12

97

LESSON 13

107

LESSON 14

113

vi

LESSON 15

FACTORING POLYNOMIALS What Is Factoring? Finding the Greatest Common Factor Factoring Using the Greatest Common Factor Method Factoring Using the Difference of Two Squares Method Factoring Using the Trinomial Method

119

LESSON 16

USING FACTORING 127 Factoring Trinomials That Have a Coefficient Other Than One for the First Term Factoring Using Any Method Factoring Using More Than One Method SOLVING QUADRATIC EQUATIONS What Is a Quadratic Equation? Solving Quadratic Equations Using Factoring SIMPLIFYING RADICALS What Is a Radical? Square Roots of Perfect Squares Simplifying Radicals Adding and Subtracting Radicals Multiplying and Dividing Radicals SOLVING RADICAL EQUATIONS What Is a Radical Equation? Solving Complex Radical Equations USING THE QUADRATIC FORMULA What Is a Quadratic Equation? What Is the Quadratic Formula? Solving Quadratic Equations That Have a Radical in the Answer 133

LESSON 17

LESSON 18

139

LESSON 19

149

LESSON 20

153

Posttest Answer Key Glossary

159 171 203

vii

Introduction

I

f you have never taken an algebra course and now find that you need to know algebra, this is the book for you. If you have already taken an algebra course but felt like you never understood what the teacher was trying to tell you, this book can teach you what you need to know. If it has been a while since you have taken an algebra course and you need to refresh your skills, this book will review the basics and reteach you the skills you may have forgotten. Whatever your reason for needing to know algebra, Algebra Success will teach you what you need to know. It gives you the basics of an Algebra I course in clear and straightforward lessons that you can complete at your own pace. Math teachers often hear the comment, I was never very good in math. If you didnt take algebra because you thought it was too hard, you will be surprised to find out how easy it is. If you took algebra but didnt understand it, when you finish this book, you wont believe how easy algebra can be. Algebra is math with variables, numbers whose actual values are not yet known. The ability to calculate with the unknown makes algebra essential for science, business, and everyday problem solving in a variety of fields. Even if you dont work in the science or technology sectors, having a good grasp of the principles of algebra can help you solve problems with easeat work, at school, or in your own life.

Overcoming Math AnxietyDo you like math, or do you find math an unpleasant experience? It is human nature for people to like what they are good at. Generally, people who dislike math have not had much success with math.

ix

INTRODUCTION

If you have struggled with math, ask yourself why. Was it because the class went too fast? Did you have a chance to understand a concept fully before you went on to a new one? Students frequently comment, I was just starting to understand, and then the teacher went on to something new. That is why Algebra Success is self-paced. You work at your own pace. You go on to a new concept only when you are ready. Algebra Success goes straight to the basics using common, everyday language. Concepts are explained in the clearest possible language so that you do not get lost in mathematical jargon. Only the algebra terms that you need to function in a basic algebra course are included. When you study the lessons in this book, the only person you have to answer to is yourself. You dont have to pretend you know something when you dont truly understand. You get to take the time you need to understand everything before you go on to the next lesson. You have truly learned something only if you thoroughly understand it. Merely completing a lesson does not mean you understand it. When you go through a lesson, work for understanding, taking as much time as you need to understand the examples. Check your work with the answer key as you progress through the lesson. If you get the right answer, you are on the right track! If you finish a lesson and you dont feel confident that you fully understand the lesson, do it again. Athletes and musicians practice a skill until they perfect it. Repetition works for mathematicians, too. Remember the adage Practice makes perfect.You might think you dont want to take the time to go back over something again. However, making sure you understand a lesson completely may save you time in future lessons. Rework problems you missed to make sure you dont make the same mistakes again. Remember, overcoming math anxiety is just another problem you can solve.

How to Use This BookAlgebra Success teaches basic algebra concepts in 20 self-paced lessons. The book also includes a pretest, a posttest, and a glossary of mathematical terms. Before you begin Lesson 1, take the pretest to assess your current algebra abilities. Youll find the answer key for the pretest at the end of the book. Each answer includes the lesson number that the problem is testing. This will be helpful in determining your strengths and weaknesses and reviewing concepts that are difficult for you. After taking the pretest, move on to Lesson 1. Each lesson offers detailed explanations of a new concept. There are numerous examples with step-by-step solutions. As you proceed through a lesson, you will find tips and shortcuts that will help you learn a concept. Each new concept is followed by a practice set of problems that allow you to practice each new concept without tedious calculations. You will find that most calculations can be done without the use of a calculator. The emphasis is on algebra conceptsnot calculations. The answers to the practice problems are in an answer key located at the end of the book. Some lessons include word problems that will illustrate real-life applications of the algebra concept that was studied in the lesson. Algebra is a tool that is used to solve many real-life problems. At the end of each lesson, an exercise called Skill Building until Next Time applies the lessons topic to an activity you may encounter in your daily life. As you work thr