Student Solutions Manual for 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 Skills



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



Review of the Real Number System

R.1 Fractions, Decimals, and Percents
R.2 Basic Concepts from Algebra
R.3 Operations on Real Numbers
R.3 Exponents, Roots, and Order of Operations
R.4 Properties of Real Numbers
Chapter R Summary
Chapter R Test


Linear Equations, Inequalities, and Applications

1.1 Linear Equations in One Variable
1.2 Formulas and Percent
1.3 Applications of Linear Equations
1.4 Further Applications of Linear Equations

Summary Exercises: Applying Problem-Solving Techniques


1.5 Linear Inequalities in One Variable
1.6 Set Operations and Compound Inequalities
1.7 Absolute Value Equations and Inequalities
Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Mixed Review Exercises
Chapter 1 Test
Chapters R and 1 Cumulative Review Exercises


Linear Equations, Graphs, and Functions

2.1 Linear Equations in Two Variables

Study Skills: Managing Your Time


2.2 The Slope of a Line
2.3 Writing Equations of Lines

Summary Exercises: Finding Slopes and Equations of Lines


2.4 Linear Inequalities in Two Variables
2.5 Introduction to Relations and Functions
2.6 Function Notation and Linear Functions
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Mixed Review Exercises
Chapter 2 Test
Chapters R–2 Cumulative Review Exercises


Systems of Linear Equations

3.1 Systems of Linear Equations in Two Variables
3.2 Systems of Linear Equations in Three Variables
3.3 Applications of Systems of Linear Equations
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Mixed Review Exercises
Chapter 3 Test
Chapters R–3 Cumulative Review Exercises


Exponents, Polynomials, and Polynomial Functions

4.1 Integer Exponents
4.2 Scientific Notation
4.3 Adding and Subtracting Polynomials
4.4 Polynomial Functions, Graphs, and Composition
4.5 Multiplying Polynomials
4.6 Dividing Polynomials
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Mixed Review Exercises
Chapter 4 Test
Chapters R–4 Cumulative Review Exercises


Factoring

5.1 Greatest Common Factors and Factoring by Grouping
5.2 Factoring Trinomials
5.3 Special Factoring
5.4 A General Approach to Factoring
5.5 Solving Equations by the Zero-Factor Property
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Mixed Review Exercises
Chapter 5 Test
Chapters R–5 Cumulative Review Exercises


Rational Expressions and Functions

6.1 Rational Expressions and Functions; Multiplying and Dividing
6.2 Adding and Subtracting Rational Expressions
6.3 Complex Fractions
6.4 Equations with Rational Expressions and Graphs

Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations


6.5 Applications of Rational Expressions
6.6 Variation
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Mixed Review Exercises
Chapter 6 Test
Chapters R–6 Cumulative Review Exercises


Roots, Radicals, and Root Functions

7.1 Radical Expressions and Graphs
7.2 Rational Exponents
7.3 Simplifying Radicals, the Distance Formula, and Circles
7.4 Adding and Subtracting Radical Expressions
7.5 Multiplying and Dividing Radical Expressions

Summary Exercises: Performing Operations with Radicals and Rational Exponents


7.6 Solving Equations with Radicals
7.7 Complex Numbers
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Mixed Review Exercises
Chapter 7 Test
Chapters R–7 Cumulative Review Exercises


Quadratic Equations, Inequalities, and Functions

8.1 The Square Root Property and Completing the Square
8.2 The Quadratic Formula
8.3 Equations That Lead to Quadratic Methods

Summary Exercises: Applying Methods for Solving Quadratic Equations


8.4 Formulas and Further Applications
8.5 Graphs of Quadratic Functions
8.6 More about Parabolas and Their Applications
8.7 Polynomial and Rational Inequalities
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Mixed Review Exercises
Chapter 8 Test
Chapters R–8 Cumulative Review Exercises


Inverse, Exponential, and Logarithmic Functions

9.1 Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithms
9.5 Common and Natural Logarithms
9.6 Exponential and Logarithmic Equations; Further Applications
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Mixed Review Exercises
Chapter 9 Test
Chapters R–9 Cumulative Review Exercises


Nonlinear Functions, Conic Sections, and Nonlinear Systems

10.1 Additional Graphs of Functions
10.2 Circles Revisited and Ellipses
10.3 Hyperbolas and Functions Defined by Radicals
10.4 Nonlinear Systems of Equations
10.5 Second-Degree Inequalities and Systems of Inequalities
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Mixed Review Exercises
Chapter 10 Test
Chapters R-10 Cumulative Review Exercises


Further Topics in Algebra

11.1 Sequences and Series
11.2 Arithmetic Sequences
11.3 Geometric Sequences
11.4 The Binomial Theorem
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Mixed Review Exercises
Chapter 11 Test
Chapters R-11 Cumulative Review Exercises



Appendix A: Synthetic Division

Answers to Selected Exercises

Credits

Index