Elementary Algebra

About our authors Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball state University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.Marvin Bittinger has taught math at the university level for more than thirty-eight years, and he is now professor emeritus of mathematics education at Indiana University-Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts–Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing, and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.

• 1. Introduction to Algebraic Expressions 1.1 Introduction to Algebra1.2 The Commutative, Associative, and Distributive Laws1.3 Fraction Notation1.4 Positive and Negative Real Numbers1.5 Addition of Real Numbers1.6 Subtraction of Real Numbers1.7 Multiplication and Division of Real Numbers1.8 Exponential Notation and Order of Operations2. Equations, Inequalities, and Problem Solving 2.1 Solving Equations2.2 Using the Principles Together2.3 Formulas2.4 Applications with Percent2.5 Problem Solving2.6 Solving Inequalities2.7 Solving Applications with Inequalities3. Introduction to Graphing 3.1 Reading Graphs, Plotting Points, and Scaling Graphs3.2 Graphing Linear Equations3.3 Graphing and Intercepts3.4 Rates3.5 Slope3.6 Slope-Intercept Form3.7 Point-Slope Form4. Polynomials 4.1 Exponents and Their Properties4.2 Polynomials4.3 Addition and Subtraction of Polynomials4.4 Multiplication of Polynomials4.5 Special Products4.6 Polynomials in Several Variables4.7 Division of Polynomials4.8 Negative Exponents and Scientific Notation5. Polynomials and Factoring 5.1 Introduction to Factoring5.2 Factoring Trinomials of the Type x2 + bx + c5.3 Factoring Trinomials of the Type ax2 + bx + c5.4 Factoring Perfect-Square Trinomials and Difference of Squares5.5 Factoring: A General Strategy5.6 Solving Quadratic Equations by Factoring5.7 Solving Applications6. Rational Expressions and Equations 6.1 Rational Expressions6.2 Multiplication and Division6.3 Addition, Subtraction, and Least Common Denominators6.4 Addition and Subtraction with Unlike Denominators6.5 Complex Rational Expressions6.6 Rational Equations6.7 Applications Using Rational Equations and Proportions7. Systems and More Graphing 7.1 Systems of Equations and Graphing7.2 Systems of Equations and Substitution7.3 Systems of Equations and Elimination7.4 More Applications Using Systems7.5 Linear Inequalities in Two Variables7.6 Systems of Linear Inequalities7.7 Direct Variation and Inverse Variation8. Radical Expressions and Equations 8.1 Introduction to Square Roots and Radical Expressions8.2 Multiplying and Simplifying Radical Expressions8.3 Quotients Involving Square Roots8.4 Radical Expressions with Several Terms8.5 Radical Equations8.6 Applications Using Right Triangles8.7 Higher Roots and Rational Exponents9. Quadratic Equations 9.1 Solving Quadratic Equations: The Principle of Square Roots9.2 Solving Quadratic Equations: Completing the Square9.3 The Quadratic Formula and Applications9.4 Formulas9.5 Complex Numbers as Solutions of Quadratic Equations9.6 Graphs of Quadratic Functions9.7 FunctionsAppendix A. Factoring Sums or Differences of Cubes Appendix B. Mean, Median, and Mode Appendix C. Sets