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.

• Preface viTo the Student xiiiLearning Styles Inventory xvThe Carson Math Study System xvii  1 Real Numbers andExpressions 1  1.1 Sets and the Structure of Algebra 21.2 Operations with Real Numbers; Propertiesof Real Numbers 121.3 Exponents, Roots, and Order ofOperations 241.4 Evaluating and Rewriting Expressions 34Summary and Review Exercises 45Practice Test 53  2 Linear Equations and Inequalitiesin One Variable 55  2.1 Linear Equations and Formulas 562.2 Solving Problems 662.3 Solving Linear Inequalities 742.4 Compound Inequalities 852.5 Equations Involving Absolute Value 962.6 Inequalities Involving AbsoluteValue 100Summary and Review Exercises 108Practice Test 116Chapters 1—2 Cumulative ReviewExercises 118  3 Equations and Inequalities in TwoVariables; Functions 120  3.1 Graphing Linear Equations 1213.2 The Slope of a Line 1333.3 The Equation of a Line 1453.4 Graphing Linear Inequalities 1563.5 Introduction to Functions and FunctionNotation 164Summary and Review Exercises 182Practice Test 192Chapters 1—3 Cumulative ReviewExercises 194  4 Systems of Linear Equationsand Inequalities 197  4.1 Solving Systems of Linear Equationsin Two Variables 1984.2 Solving Systems of Linear Equationsin Three Variables 2164.3 Solving Applications Using Systemsof Equations 2234.4 Solving Systems of Linear EquationsUsing Matrices 2364.5 Solving Systems of Linear Inequalities 245Summary and Review Exercises 252Practice Test 259Chapters 1—4 Cumulative ReviewExercises 261  5 Exponents, Polynomials, andPolynomial Functions 2635.1 Exponents and Scientific Notation 2645.2 Polynomials and Polynomial Functions 2805.3 Multiplying Polynomials 2945.4 Dividing Polynomials 3055.5 Synthetic Division and the RemainderTheorem 313Summary and Review Exercises 319Practice Test 327Chapters 1—5 Cumulative ReviewExercises 329  6 Factoring 3316.1 Greatest Common Factor andFactoring by Grouping 3326.2 Factoring Trinomials 3406.3 Factoring Special Productsand Factoring Strategies 3506.4 Solving Equations by Factoring 361Summary and Review Exercises 374Practice Test 381Chapters 1—6 Cumulative ReviewExercises 383  7 Rational Expressions andEquations 3867.1 Simplifying, Multiplying, and DividingRational Expressions 3877.2 Adding and Subtracting RationalExpressions 4027.3 Simplifying Complex RationalExpressions 4147.4 Solving Equations Containing RationalExpressions 4237.5 Applications with Rational Expressions;Variation 430Summary and Review Exercises 444Practice Test 456Chapters 1—7 Cumulative ReviewExercises 458  8 Rational Exponents, Radicals,and Complex Numbers 460  8.1 Radical Expressions and Functions 4618.2 Rational Exponents 4718.3 Multiplying, Dividing, and SimplifyingRadicals 4818.4 Adding, Subtracting, and MultiplyingRadical Expressions 4898.5 Rationalizing Numerators and Denominatorsof Radical Expressions 4968.6 Radical Equations and Problem Solving 5068.7 Complex Numbers 515Summary and Review Exercises 523Practice Test 533Chapters 1—8 Cumulative ReviewExercises 535  9 Quadratic Equations andFunctions 537  9.1 The Square Root Principle and Completingthe Square 5389.2 Solving Quadratic Equations Using theQuadratic Formula 5489.3 Solving Equations That Are Quadraticin Form 5599.4 Graphing Quadratic Functions 5689.5 Solving Nonlinear Inequalities 580Summary and Review Exercises 591Practice Test 598Chapters 1—9 Cumulative ReviewExercises 601  10 Exponential and LogarithmicFunctions 603  10.1 Composite and Inverse Functions 60410.2 Exponential Functions 61610.3 Logarithmic Functions 62510.4 Properties of Logarithms 63310.5 Common and Natural Logarithms 64110.6 Exponential and Logarithmic Equations withApplications 646Summary and Review Exercises 657Practice Test 669Chapters 1—10 Cumulative ReviewExercises 671  11 Conic Sections 673  11.1 Parabolas and Circles 67411.2 Ellipses and Hyperbolas 68711.3 Nonlinear Systems of Equations 69811.4 Nonlinear Inequalities and Systems ofInequalities 704Summary and Review Exercises 711Practice Test 720Chapters 1—11 Cumulative ReviewExercises 722Appendixes 673  A. Arithmetic Sequences and Series APP-1B. Geometric Sequences and Series APP-8C. The Binomial Theorem APP-15D. Solving Systems of Linear EquationsUsing Cramer’s Rule APP-20E. Permutations and Combinations(available online via MyMathLab)F. Probability(available online via MyMathLab)  Photo Credits P-1Collaborative Exercises C-1Answers A-1Glossary G-1Index of Applications IA-1Index I-1