Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

An open source (CC-BY) textbook Available for free download at:

by Tyler Wallace

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ISBN #978-1-4583-7768-5 Copyright 2010, Some Rights Reserved CC-BY.

Beginning and Intermediate Algebra by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. () Based on a work at .

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Special thanks to: My beautiful wife, Nicole Wallace who spent countless hours typing problems and my two wonderful kids for their patience and support during this project

Another thanks goes to the faculty reviewers who reviewed this text: Donna Brown, Michelle Sherwood, Ron Wallace, and Barbara Whitney One last thanks to the student reviewers of the text: Eloisa Butler, Norma Cabanas, Irene Chavez, Anna Dahlke, Kelly Diguilio, Camden Eckhart, Brad Evers, Lisa Garza, Nickie Hampshire, Melissa Hanson, Adriana Hernandez, Tiffany Isaacson, Maria Martinez, Brandon Platt, Tim Ries, Lorissa Smith, Nadine Svopa, Cayleen Trautman, and Erin White

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Table of Contents

Chapter 0: Pre-Algebra 0.1 Integers.........................................7 0.2 Fractions.....................................12 0.3 Order of Operations....................18 0.4 Properties of Algebra..................22 Chapter 1: Solving Linear Equations 1.1 One-Step Equations....................28 1.2 Two-Step Equations....................33 1.3 General Linear Equations...........37 1.4 Solving with Fractions................43 1.5 Formulas.....................................47 1.6 Absolute Value Equations...........52 1.7 Variation.....................................57 1.8 Application: Number/Geometry.64 1.9 Application: Age.........................72 1.10 Application: Distance................79 Chapter 2: Graphing 2.1 Points and Lines.........................89 2.2 Slope...........................................95 2.3 Slope-Intercept Form................102 2.4 Point-Slope Form......................107 2.5 Parallel & Perpendicular Lines.112

Chapter 3: Inequalities 3.1 Solve and Graph Inequalities....118 3.2 Compound Inequalitites............124 3.3 Absolute Value Inequalities.......128 Chapter 4: Systems of Equations 4.1 Graphing...................................134 4.2 Substitution..............................139 4.3 Addition/Elimination................146 4.4 Three Variables.........................151 4.5 Application: Value Problems.....158 4.6 Application: Mixture Problems.167 Chapter 5: Polynomials 5.1 Exponent Properties.................177 5.2 Negative Exponents..................183 5.3 Scientific Notation.....................188 5.4 Introduction to Polynomials.....192 5.5 Multiply Polynomials................196 5.6 Multiply Special Products.........201 5.7 Divide Polynomials...................205

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Chapter 6: Factoring 6.1 Greatest Common Factor..........212 6.2 Grouping...................................216 6.3 Trinomials where a = 1..............221 6.4 Trinomials where a 1..............226 6.5 Factoring Special Products.......229 6.6 Factoring Strategy....................234 6.7 Solve by Factoring.....................237 Chapter 7: Rational Expressions 7.1 Reduce Rational Expressions....243 7.2 Multiply and Divide..................248 7.3 Least Common Denominator....253 7.4 Add and Subtract.....................257 7.5 Complex Fractions....................262 7.6 Proportions...............................268 7.7 Solving Rational Equations.......274 7.8 Application: Dimensional Analysis....279 Chapter 8: Radicals 8.1 Square Roots.............................288 8.2 Higher Roots.............................292 8.3 Adding Radicals........................295 8.4 Multiply and Divide Radicals...298 8.5 Rationalize Denominators.........303 8.6 Rational Exponents...................310 8.7 Radicals of Mixed Index...........314 8.8 Complex Numbers.....................318

Chapter 9: Quadratics 9.1 Solving with Radicals................326 9.2 Solving with Exponents............332 9.3 Complete the Square.................337 9.4 Quadratic Formula....................343 9.5 Build Quadratics From Roots...348 9.6 Quadratic in Form....................352 9.7 Application: Rectangles............357 9.8 Application: Teamwork.............364 9.9 Simultaneous Products.............370 9.10 Application: Revenue and Distance.373 9.11 Graphs of Quadratics..............380 Chapter 10: Functions 10.1 Function Notation...................386 10.2 Operations on Functions.........393 10.3 Inverse Functions....................401 10.4 Exponential Functions.............406 10.5 Logarithmic Functions............410 10.6 Application: Compound Interest.414 10.7 Trigonometric Functions.........420 10.8 Inverse Trigonometric Functions.428 Answers........................................438

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