Elementary and Intermediate Algebra

Tom Carson ’s first teaching experience was teaching guitar while an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study System. In addition to his work on the Carson Developmental Algebra Series, Tom also is the author of Prealgebra, Fourth Edition.Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Bill has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In addition to his work on the Carson series, Bill is also the lead author of Integrated Algebra and Arithmetic, 2/e, also published by Pearson. In his spare time, he enjoys fishing, traveling, and hiking.

• Table of Contents Foundations of Algebra 1.1 Number Sets and the Structure of Algebra1.2 Fractions1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers1.5 Exponents, Roots, and Order of Operations1.6 Translating Word Phrases to Expressions1.7 Evaluating and Rewriting ExpressionsSolving Linear Equations and Inequalities 2.1 Equations, Formulas, and the Problem-Solving Process2.2 The Addition Principle of Equality2.3 The Multiplication Principle of Equality2.4 Applying the Principles to Formulas2.5 Translating Word Sentences to Equations2.6 Ratios and Proportions2.7 Percents2.8 Solving Linear InequalitiesGraphing Linear Equations and Inequalities 3.1 The Rectangular Coordinate System3.2 Graphing Linear Equations3.3 Graphing Using Intercepts3.4 Slope–Intercept Form3.5 Point–Slope Form3.6 Graphing Linear Inequalities3.7 Introduction to Functions and Function NotationSystems of Linear Equations and Inequalities 4.1 Solving Systems of Linear Equations Graphically4.2 Solving Systems of Linear Equations by Substitution; Applications4.3 Solving Systems of Linear Equations by Elimination; Applications4.4 Solving Systems of Linear Equations in Three Variables; Applications4.5 Solving Systems of Linear Equations Using Matrices4.6 Solving Systems of Linear InequalitiesPolynomials 5.1 Exponents and Scientific Notation5.2 Introduction to Polynomials5.3 Adding and Subtracting Polynomials5.4 Exponent Rules and Multiplying Monomials5.5 Multiplying Polynomials; Special Products5.6 Exponent Rules and Dividing PolynomialsFactoring 6.1 Greatest Common Factor and Factoring by Grouping6.2 Factoring Trinomials of the Form x2 + bx + c6.3 Factoring Trinomials of the Form ax2 + bx + c, where a ≠ 16.4 Factoring Special Products6.5 Strategies for Factoring6.6 Solving Quadratic Equations by Factoring6.7 Graphs of Quadratic Equations and FunctionsRational Expressions and Equations 7.1 Simplifying Rational Expressions7.2 Multiplying and Dividing Rational Expressions7.3 Adding and Subtracting Rational Expressions with the Same Denominator7.4 Adding and Subtracting Rational Expressions with Different Denominators7.5 Complex Rational Expressions7.6 Solving Equations Containing Rational Expressions7.7 Applications with Rational Expressions, Including VariationMore on Inequalities, Absolute Value, and Functions 8.1 Compound Inequalities8.2 Equations Involving Absolute Value; Absolute Value Functions8.3 Inequalities Involving Absolute ValueRational Exponents, Radicals, and Complex Numbers 9.1 Radical Expressions and Functions9.2 Rational Exponents9.3 Multiplying, Dividing, and Simplifying Radicals9.4 Adding, Subtracting, and Multiplying Radical Expressions9.5 Rationalizing Numerators and Denominators of Radical Expressions9.6 Radical Equations and Problem Solving9.7 Complex NumbersQuadratic Equations and Functions 10.1 The Square Root Principle and Completing the Square10.2 Solving Quadratic Equations Using the Quadratic Formula10.3 Solving Equations That Are Quadratic in Form10.4 Graphing Quadratic Functions10.5 Solving Nonlinear Inequalities10.6 Function OperationsExponential and Logarithmic Functions 11.1 Composite and Inverse Functions11.2 Exponential Functions11.3 Logarithmic Functions11.4 Properties of Logarithms11.5 Common and Natural Logarithms11.6 Exponential and Logarithmic Equations with ApplicationsConic Sections 12.1 Parabolas and Circles12.2 Ellipses and Hyperbolas12.3 Nonlinear Systems of Equations12.4 Nonlinear Inequalities and Systems of InequalitiesR. Elementary Algebra ReviewAppendices Mean, Median, and ModeArithmetic Sequences and SeriesGeometric Sequences and SeriesThe Binomial TheoremSynthetic DivisionSolving Systems of Linear Equations Using Cramer’s Rule