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 Text
Study Skill 2: Reading Your Math Text
Study Skill 3: Taking Lecture Notes
Study Skill 4: Completing Your Homework
Study Skill 5: Using Study Cards
Study Skill 6: Managing Your Time
Study Skill 7: Reviewing a Chapter
Study Skill 8: Taking Math Tests
Study Skill 9: Analyzing Your Test Results
Study Skill 10: Preparing for Your Math Final

R. Prealgebra Review

R.1 Fractions
R.2 Decimals and Percents

1. The Real Number System

1.1 Exponents, Order of Operations, and Inequality
1.2 Variables, Expressions, and Equations
1.3 Real Numbers and the Number Line
1.4 Adding and Subtracting Real Numbers
1.5 Multiplying and Dividing Real Numbers
Summary Exercises: Performing Operations with Real Numbers
1.6 Properties of Real Numbers
1.7 Simplifying Expressions
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Mixed Review Exercises
Chapter 1 Test
Chapters R and 1 Cumulative Review Exercises

2. Linear Equations and Inequalities in One Variable

2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Solving Linear Equations Using Both Properties of Equality
2.4 Clearing Fractions and Decimals When Solving Linear Equations
Summary Exercises: Applying Methods for Solving Linear Equations
2.5 Applications of Linear Equations
2.6 Formulas and Additional Applications from Geometry
2.7 Ratio, Proportion, and Percent
2.8 Further Applications of Linear Equations
2.9 Solving Linear Inequalities
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Mixed Review Exercises
Chapter 2 Test
Chapters R-2 Cumulative Review Exercises

3. Linear Equations in Two Variables

3.1 Linear Equations and Rectangular Coordinates
3.2 Graphing Linear Equations in Two Variables
3.3 The Slope of a Line
3.4 Slope-Intercept Form of a Linear Equation
3.5 Point-Slope Form of a Linear Equation and Modeling
Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Mixed Review Exercises
Chapter 3 Test
Chapters R-3 Cumulative Review Exercises

4. Exponents and Polynomials

4.1 The Product Rule and Power Rules for Exponents
4.2 Integer Exponents and the Quotient Rule
Summary Exercises: Applying the Rules for Exponents
4.3 Scientific Notation
4.4 Adding, Subtracting, and Graphing Polynomials
4.5 Multiplying Polynomials
4.6 Special Products
4.7 Dividing Polynomials
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Mixed Review Exercises
Chapter 4 Test
Chapters R-4 Cumulative Review Exercises

5. Factoring and Applications

5.1 Greatest Common Factor; Factoring by Grouping
5.2 Factoring Trinomials
5.3 More on Factoring Trinomials
5.4 Special Factoring Techniques
Summary Exercises: Recognizing and Applying Factoring Strategies
5.5 Solving Quadratic Equations Using the Zero-Factor Property
5.6 Applications of Quadratic Equations
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Mixed Review Exercises
Chapter 5 Test
Chapters R-5 Cumulative Review Exercises

6. Rational Expressions and Applications

6.1 The Fundamental Property of Rational Expressions
6.2 Multiplying and Dividing Rational Expressions
6.3 Least Common Denominators
6.4 Adding and Subtracting Rational Expressions
6.5 Complex Fractions
6.6 Solving Equations with Rational Expressions
Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations
6.7 Applications of Rational Expressions
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Mixed Review Exercises
Chapter 6 Test
Chapters R-6 Cumulative Review Exercises

7. Linear Equations, Graphs, and Systems

7.1 Review of Graphs and Slopes of Lines
7.2 Review of Equations of Lines; Linear Models
7.3 Solving Systems of Linear Equations by Graphing
7.4 Solving Systems of Linear Equations by Substitution
7.5 Solving Systems of Linear Equations by Elimination
Summary Exercises: Applying Techniques for Solving Systems of Linear Equations
7.6 Systems of Linear Equations in Three Variables
7.7 Applications of Systems of Linear Equations
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Mixed Review Exercises
Chapter 7 Test
Chapters R-7 Cumulative Review Exercises

8. Inequalities and Absolute Value

8.1 Review of Linear Inequalities in One Variable
8.2 Set Operations and Compound Inequalities
8.3 Absolute Value Equations and Inequalities
Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities
8.4 Linear Inequalities and Systems in Two Variables
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Mixed Review Exercises
Chapter 8 Test
Chapters R-8 Cumulative Review Exercises

9. Relations and Functions

9.1 Introduction to Relations and Functions
9.2 Function Notation and Linear Functions
9.3 Polynomial Functions, Operations, and Composition
9.4 Variation
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Mixed Review Exercises
Chapter 9 Test
Chapters R-9 Cumulative Review Exercises

10. Roots, Radicals, and Root Functions

10.1 Radical Expressions and Graphs
10.2 Rational Exponents
10.3 Simplifying Radicals, the Distance Formula, and Circles
10.4 Adding and Subtracting Radical Expressions
10.5 Multiplying and Dividing Radical Expressions
Summary Exercises: Performing Operations with Radicals and Rational Exponents
10.6 Solving Equations with Radicals
10.7 Complex Numbers
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Mixed Review Exercises
Chapter 10 Test
Chapters R-10 Cumulative Review Exercises

11. Quadratic Equations, Inequalities, and Functions

11.1 Solving Quadratic Equations by the Square Root Property
11.2 Solving Quadratic Equations by Completing the Square
11.3 Solving Quadratic Equations by the Quadratic Formula
11.4 Equations That Lead to Quadratic Methods
Summary Exercises: Applying Methods for Solving Quadratic Equations
11.5 Formulas and Further Applications
11.6 Graphs of Quadratic Functions
11.7 More about Parabolas and Their Applications
11.8 Polynomial and Rational Inequalities
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Mixed Review Exercises
Chapter 11 Test
Chapters R-11 Cumulative Review Exercises

12. Inverse, Exponential, and Logarithmic Functions

12.1 Inverse Functions
12.2 Exponential Functions
12.3 Logarithmic Functions
12.4 Properties of Logarithms
12.5 Common and Natural Logarithms
12.6 Exponential and Logarithmic Equations; Further Applications
Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Mixed Review Exercises
Chapter 12 Test
Chapters R-12 Cumulative Review Exercises

13. Nonlinear Functions, Conic Sections, and Nonlinear Systems

13.1 Additional Graphs of Functions
13.2 Circles Revisited and Ellipses
13.3 Hyperbolas and Functions Defined by Radicals
13.4 Nonlinear Systems of Equations
13.5 Second-Degree Inequalities and Systems of Inequalities
Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Mixed Review Exercises
Chapter 13 Test
Chapters R-13 Cumulative Review Exercises

14. Further Topics in Algebra

14.1 Sequences and Series
14.2 Arithmetic Sequences
14.3 Geometric Sequences
14.4 The Binomial Theorem
Chapter 14 Summary
Chapter 14 Review Exercises
Chapter 14 Mixed Review Exercises
Chapter 14 Test
Chapters R-14 Cumulative Review Exercises