Student Solutions Manual for Beginning & Intermediate Algebra

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.  When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.  A native Midwesterner, Terry McGinnis received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.  Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks where she earned a bachelor’s degree in Secondary Mathematics Education. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Louis. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding. She is able to pursue these interests as a contributor on the Lial Developmental Math series, and a co-author on the Precalculus series.

• Study Skill 1: Using Your Math TextStudy Skill 2: Reading Your Math TextStudy Skill 3: Taking Lecture NotesStudy Skill 4: Completing Your HomeworkStudy Skill 5: Using Study CardsStudy Skill 6: Managing Your TimeStudy Skill 7: Reviewing a ChapterStudy Skill 8: Taking Math TestsStudy Skill 9: Analyzing Your Test ResultsStudy Skill 10: Preparing for Your Math FinalR. Prealgebra Review R.1 FractionsR.2 Decimals and Percents1. The Real Number System 1.1 Exponents, Order of Operations, and Inequality1.2 Variables, Expressions, and Equations1.3 Real Numbers and the Number Line1.4 Adding and Subtracting Real Numbers1.5 Multiplying and Dividing Real NumbersSummary Exercises: Performing Operations with Real Numbers1.6 Properties of Real Numbers1.7 Simplifying ExpressionsChapter 1 SummaryChapter 1 Review ExercisesChapter 1 Mixed Review ExercisesChapter 1 TestChapters R and 1 Cumulative Review Exercises2. Linear Equations and Inequalities in One Variable 2.1 The Addition Property of Equality2.2 The Multiplication Property of Equality2.3 Solving Linear Equations Using Both Properties of Equality2.4 Clearing Fractions and Decimals When Solving Linear EquationsSummary Exercises: Applying Methods for Solving Linear Equations2.5 Applications of Linear Equations2.6 Formulas and Additional Applications from Geometry2.7 Ratio, Proportion, and Percent2.8 Further Applications of Linear Equations2.9 Solving Linear InequalitiesChapter 2 SummaryChapter 2 Review ExercisesChapter 2 Mixed Review ExercisesChapter 2 TestChapters R-2 Cumulative Review Exercises3. Linear Equations in Two Variables 3.1 Linear Equations and Rectangular Coordinates3.2 Graphing Linear Equations in Two Variables3.3 The Slope of a Line3.4 Slope-Intercept Form of a Linear Equation3.5 Point-Slope Form of a Linear Equation and ModelingSummary Exercises: Applying Graphing and Equation-Writing Techniques for LinesChapter 3 SummaryChapter 3 Review ExercisesChapter 3 Mixed Review ExercisesChapter 3 TestChapters R-3 Cumulative Review Exercises4. Exponents and Polynomials 4.1 The Product Rule and Power Rules for Exponents4.2 Integer Exponents and the Quotient RuleSummary Exercises: Applying the Rules for Exponents4.3 Scientific Notation4.4 Adding, Subtracting, and Graphing Polynomials4.5 Multiplying Polynomials4.6 Special Products4.7 Dividing PolynomialsChapter 4 SummaryChapter 4 Review ExercisesChapter 4 Mixed Review ExercisesChapter 4 TestChapters R-4 Cumulative Review Exercises5. Factoring and Applications 5.1 Greatest Common Factor; Factoring by Grouping5.2 Factoring Trinomials5.3 More on Factoring Trinomials5.4 Special Factoring TechniquesSummary Exercises: Recognizing and Applying Factoring Strategies5.5 Solving Quadratic Equations Using the Zero-Factor Property5.6 Applications of Quadratic EquationsChapter 5 SummaryChapter 5 Review ExercisesChapter 5 Mixed Review ExercisesChapter 5 TestChapters R-5 Cumulative Review Exercises6. Rational Expressions and Applications 6.1 The Fundamental Property of Rational Expressions6.2 Multiplying and Dividing Rational Expressions6.3 Least Common Denominators6.4 Adding and Subtracting Rational Expressions6.5 Complex Fractions6.6 Solving Equations with Rational ExpressionsSummary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations6.7 Applications of Rational ExpressionsChapter 6 SummaryChapter 6 Review ExercisesChapter 6 Mixed Review ExercisesChapter 6 TestChapters R-6 Cumulative Review Exercises7. Linear Equations, Graphs, and Systems 7.1 Review of Graphs and Slopes of Lines7.2 Review of Equations of Lines; Linear Models7.3 Solving Systems of Linear Equations by Graphing7.4 Solving Systems of Linear Equations by Substitution7.5 Solving Systems of Linear Equations by EliminationSummary Exercises: Applying Techniques for Solving Systems of Linear Equations7.6 Systems of Linear Equations in Three Variables7.7 Applications of Systems of Linear EquationsChapter 7 SummaryChapter 7 Review ExercisesChapter 7 Mixed Review ExercisesChapter 7 TestChapters R-7 Cumulative Review Exercises8. Inequalities and Absolute Value 8.1 Review of Linear Inequalities in One Variable8.2 Set Operations and Compound Inequalities8.3 Absolute Value Equations and InequalitiesSummary Exercises: Solving Linear and Absolute Value Equations and Inequalities8.4 Linear Inequalities and Systems in Two VariablesChapter 8 SummaryChapter 8 Review ExercisesChapter 8 Mixed Review ExercisesChapter 8 TestChapters R-8 Cumulative Review Exercises9. Relations and Functions 9.1 Introduction to Relations and Functions9.2 Function Notation and Linear Functions9.3 Polynomial Functions, Operations, and Composition9.4 VariationChapter 9 SummaryChapter 9 Review ExercisesChapter 9 Mixed Review ExercisesChapter 9 TestChapters R-9 Cumulative Review Exercises10. Roots, Radicals, and Root Functions 10.1 Radical Expressions and Graphs10.2 Rational Exponents10.3 Simplifying Radicals, the Distance Formula, and Circles10.4 Adding and Subtracting Radical Expressions10.5 Multiplying and Dividing Radical ExpressionsSummary Exercises: Performing Operations with Radicals and Rational Exponents10.6 Solving Equations with Radicals10.7 Complex NumbersChapter 10 SummaryChapter 10 Review ExercisesChapter 10 Mixed Review ExercisesChapter 10 TestChapters R-10 Cumulative Review Exercises11. Quadratic Equations, Inequalities, and Functions 11.1 Solving Quadratic Equations by the Square Root Property11.2 Solving Quadratic Equations by Completing the Square11.3 Solving Quadratic Equations by the Quadratic Formula11.4 Equations That Lead to Quadratic MethodsSummary Exercises: Applying Methods for Solving Quadratic Equations11.5 Formulas and Further Applications11.6 Graphs of Quadratic Functions11.7 More about Parabolas and Their Applications11.8 Polynomial and Rational InequalitiesChapter 11 SummaryChapter 11 Review ExercisesChapter 11 Mixed Review ExercisesChapter 11 TestChapters R-11 Cumulative Review Exercises12. Inverse, Exponential, and Logarithmic Functions 12.1 Inverse Functions12.2 Exponential Functions12.3 Logarithmic Functions12.4 Properties of Logarithms12.5 Common and Natural Logarithms12.6 Exponential and Logarithmic Equations; Further ApplicationsChapter 12 SummaryChapter 12 Review ExercisesChapter 12 Mixed Review ExercisesChapter 12 TestChapters R-12 Cumulative Review Exercises13. Nonlinear Functions, Conic Sections, and Nonlinear Systems 13.1 Additional Graphs of Functions13.2 Circles Revisited and Ellipses13.3 Hyperbolas and Functions Defined by Radicals13.4 Nonlinear Systems of Equations13.5 Second-Degree Inequalities and Systems of InequalitiesChapter 13 SummaryChapter 13 Review ExercisesChapter 13 Mixed Review ExercisesChapter 13 TestChapters R-13 Cumulative Review Exercises14. Further Topics in Algebra 14.1 Sequences and Series14.2 Arithmetic Sequences14.3 Geometric Sequences14.4 The Binomial TheoremChapter 14 SummaryChapter 14 Review ExercisesChapter 14 Mixed Review ExercisesChapter 14 TestChapters R-14 Cumulative Review Exercises