Introductory Algebra

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers. My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students. Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics. I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students. Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra. I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.

• Introductory Algebra, 3rd Edition RReference R.1Study TipsR.2FractionsR.3Decimals and PercentsR.4Introduction to Geometry1The Set of Real Numbers 1.1Introduction to Algebra and the Set of Real Numbers1.2Exponents, Square Roots, and the Order of Operations1.3Addition of Real Numbers1.4Subtraction of Real NumbersPRE: Addition and Subtraction of Real Numbers1.5Multiplication and Division of Real Numbers1.6Properties of Real Numbers and Simplifying ExpressionsGroup Activity: Evaluating Formulas Using a Calculator2Linear Equations and Inequalities 2.1Addition, Subtraction, Multiplication, and Division Properties of Equality2.2Solving Linear Equations2.3Linear Equations: Clearing Fractions and DecimalsPRE: Equations and Expressions2.4Applications of Linear Equations:Introduction to Problem Solving2.5Applications Involving Percents2.6Literal Equations and Applications of Geometry2.7Mixture Applications and Uniform Motion2.8Linear InequalitiesGroup Activity: Computing Body Mass Index (BMI)3Graphing Linear Equations in Two Variables 3.1Rectangular Coordinate System3.2Linear Equations in Two Variables3.3Slope of a Line and Rate of Change3.4Slope-Intercept Form of a Linear EquationPRE: Linear Equations in Two Variables3.5Point-Slope Formula3.6Applications of Linear Equations and ModelingGroup Activity: Modeling a Linear Equation4Systems of Linear Equations in Two Variables 4.1Solving Systems of Equations by the Graphing Method4.2Solving Systems of Equations by the Substitution Method4.3Solving Systems of Equations by the Addition MethodPRE: Systems of Equations4.4Applications of Linear Inequalities in Two Variables4.5Linear Inequalities and Systems of Inequalities in Two VariablesGroup Activity: Creating Linear Models from Data5Polynomials and Properties of Exponents 5.1Multiplying and Dividing Expressions with Common Bases5.2More Properties of Exponents5.3Definitions of b^0 and b^-nPRE: Properties of Exponents5.4Scientific Notation5.5Addition and Subtraction of Polynomials5.6Multiplication of Polynomials and Special Products5.7Division of PolynomialsPRE: Operations on PolynomialsGroup Activity: The Pythagorean Theorem and a Geometric 'Proof'6Factoring Polynomials 6.1Greatest Common Factor and Factoring by Grouping6.2Factoring Trinomials of the Form x^2 + bx + c6.3Factoring Trinomials: Trial and Error Method6.4Factoring Trinomials: A-C Method6.5Difference of Squares and Perfect Square Trinomials6.6Sum and Difference of CubesPRE: Factoring Strategy6.7Solving Equations Using the Zero Product RulePRE: Polynomial Expressions versus PolynomialEquations6.8Applications of Quadratic EquationsGroup Activity: Building a Factoring Test7Rational Expressions and Equations 7.1Introduction to Rational Expressions7.2Multiplication and Division of Rational Expressions7.3Least Common Denominator7.4Addition and Subtraction of Rational ExpressionsPRE: Operations on Rational Expressions7.5Complex Fractions7.6Rational EquationsPRE: Comparing Rational Equations and Rational Expressions7.7Applications of Rational Equations and Proportions7.8VariationGroup Activity: Computing Monthly Mortgage Payments8Radicals 8.1Introduction to Roots and Radicals8.2Simplifying Radicals8.3Addition and Subtraction of Radicals8.4Multiplication of Radicals8.5Division of Radicals and RationalisationPRE: Operations on Radicals8.6Radicals Equations8.7Rational ExponentsGroup Activity: Calculating Standard Deviation9More Quadratic Equations 9.1The Square Root Property9.2Completing the Square9.3Quadratic FormulaPRE: Solving Different Types of Equations9.4Graphing Quadratic Equations9.5Introduction to FunctionsGroup Activity: Maximising VolumeAdditional Topics Appendix A.1Converting Units of Measurement