Introductory & 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.

Table of Contents

R. Prealgebra Review
R.1 Fractions
R.2 Decimals and Percents
Study Skills Using Your Math Text



The Real Number System

1.1 Exponents, Order of Operations, and Inequality

Study Skills Taking Lecture Notes


1.2 Variables, Expressions, and Equations

Study Skills Reading Your Math Text


1.3 Real Numbers and the Number Line

Study Skills Using Study Cards


1.4 Adding Real Numbers
1.5 Subtracting Real Numbers

Study Skills Completing Your Homework


1.6 Multiplying and Dividing Real Numbers

Summary Exercises Performing Operations with Real Numbers


1.7 Properties of Real Numbers
1.8 Simplifying Expressions

Study Skills Reviewing a Chapter




Equations, Inequalities, and Applications

2.1 The Addition Property of Equality

Study Skills Managing Your Time


2.2 The Multiplication Property of Equality
2.3 More on Solving Linear Equations

Study Skills Using Study Cards Revisited
Summary Exercises Applying Methods for Solving Linear Equations


2.4 An Introduction to Applications of Linear Equations
2.5 Formulas and Additional Applications from Geometry
2.6 Ratio, Proportion, and Percent

Summary Exercises Applying Problem-Solving Techniques


2.7 Solving Linear Inequalities

Study Skills Taking Math Tests




Graphs of Linear Equations and Inequalities in Two Variables

3.1 Linear Equations and Rectangular Coordinates

Study Skills Analyzing Your Test Results


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
Study Skills Preparing for Your Math Final Exam


3.6 Graphing Linear Inequalities in Two Variables


Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Elimination

Summary Exercises Applying Techniques for Solving Systems of Linear Equations


4.4 Applications of Linear Systems
4.5 Solving Systems of Linear Inequalities


Exponents and Polynomials

5.1 The Product Rule and Power Rules for Exponents
5.2 Integer Exponents and the Quotient Rule

Summary Exercises Applying the Rules for Exponents


5.3 An Application of Exponents: Scientific Notation
5.4 Adding and Subtracting Polynomials
5.5 Multiplying Polynomials
5.6 Special Products
5.7 Dividing a Polynomial by a Monomial
5.8 Dividing a Polynomial by a Polynomial


Factoring and Applications

6.1 Greatest Common Factors; Factor by Grouping
6.2 Factoring Trinomials
6.3 Factoring Trinomials by Grouping
6.4 Factoring Trinomials Using the FOIL Method
6.5 Special Factoring Techniques
6.6 A General Approach to Factoring
6.7 Solving Quadratic Equations Using the Zero-Factor Property
6.8 Applications of Quadratic Equations


Rational Expressions and Applications

7.1 The Fundamental Property of Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Least Common Denominators
7.4 Adding and Subtracting Rational Expressions
7.5 Complex Fractions
7.6 Solving Equations with Rational Expressions

Summary Exercises Simplifying Rational Expressions vs. Solving Rational Equations


7.7 Applications of Rational Expressions
7.8 Variation


Equations, Inequalities, Graphs, and Systems Revisited

8.1 Review of Solving Linear Equations and 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 Review of Graphing Linear Equations in Two Variables; Slope
8.6 Systems of Linear Equations in Three Variables; Applications


Relations and Functions

9.1 Introduction to Relations and Functions
9.2 Function Notation and Linear Functions
9.3 Polynomial Functions, Operations, and Graphs
9.4 Variation


Roots, Radicals, and Root Functions

10.1 Radical Expressions and Graphs
10.2 Rational Exponents
10.3 Simplifying Radical Expressions
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


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 Quadratic in Form

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


Inverse, Exponential, and Logarithmic Functions

12.1 Composition of Functions
12.2 Inverse Functions
12.3 Exponential Functions
12.4 Logarithmic Functions
12.5 Properties of Logarithms
12.6 Common and Natural Logarithms
12.7 Exponential and Logarithmic Equations and Their Applications


Nonlinear Functions, Conic Sections, and Nonlinear Systems

13.1 Additional Graphs of Functions
13.2 Circles 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



Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra) Appendix B: Synthetic Division Appendix C: Solving Systems of Linear Equations by Matrix Methods Answers to Selected Exercises Index