Student Solutions Manual for Algebra for College Students

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



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


Study Skills: Reviewing a Chapter
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
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 and Scientific Notation
4.2 Adding and Subtracting Polynomials
4.3 Polynomial Functions, Graphs, and Composition
4.4 Multiplying Polynomials
4.5 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 and Inequalities

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 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


Additional Graphs of Functions and Relations

9.1 Review of Operations and Composition
9.2 Graphs of Quadratic Functions
9.3 More About Parabolas and Their Applications
9.4 Symmetry; Increasing and Decreasing Functions
9.5 Piecewise Linear Functions
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Mixed Review Exercises
Chapter 9 Test
Chapters R–9 Cumulative Review Exercises


Inverse, Exponential, and Logarithmic Functions

10.1 Inverse Functions
10.2 Exponential Functions
10.3 Logarithmic Functions
10.4 Properties of Logarithms
10.5 Common and Natural Logarithms
10.6 Exponential and Logarithmic Equations; Further Applications
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Mixed Review Exercises
Chapter 10 Test
Chapters R–10 Cumulative Review Exercises


Polynomial and Rational Functions

11.1 Zeros of Polynomial Functions (I)
11.2 Zeros of Polynomial Functions (II)
11.3 Graphs and Applications of Polynomial Functions

Summary Exercises: Examining Polynomial Functions and Graphs


11.4 Graphs and Applications of Rational Functions
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Mixed Review Exercises
Chapter 11 Test
Chapters R–11 Cumulative Review Exercises


Conic Sections and Nonlinear Systems

12.1 Circles Revisited and Ellipses
12.2 Hyperbolas and Functions Defined by Radicals
12.3 Nonlinear Systems of Equations
12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming
Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Mixed Review Exercises
Chapter 12 Test
Chapters R–12 Cumulative Review Exercises


Further Topics in Algebra

13.1 Sequences and Series
13.2 Arithmetic Sequences
13.3 Geometric Sequences
13.4 The Binomial Theorem
13.5 Mathematical Induction
13.6 Counting Theory
13.7 Basics of Probability
Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Mixed Review Exercises
Chapter 13 Test
Chapters R–13 Cumulative Review Exercises



Appendices

A. Solving Systems of Linear Equations by Matrix Methods
B. Determinants and Cramer’s Rule
C. Properties of Matrices
D. Matrix Inverses
Photo Credits

Answers to Selected Exercises

Index