Introductory Algebra

Marge Lial (late) became interested in math at an early age–it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself 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. She was particularly interested in archeology; trips to various digs and ruin sites produced 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. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed.   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). He has been a rabid 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 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 that includes Introductory Algebra, Intermediate Algebra, and Introductory and Intermediate Algebra. 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.

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 Real Numbers

1.5 Subtracting Real Numbers

1.6 Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

 

2. Equations, Inequalities, and Applications

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 More on 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

2.7 Solving Linear Inequalities

 

3. Graphs of Linear Equations and Inequalities in Two Variables

3.1 Linear Equations in Two Variables; The Rectangular Coordinate System

3.2 Graphing Linear Equations in Two Variables

3.3 The Slope of a Line

3.4 Writing and Graphing Equations of Lines

3.5 Graphing Linear Inequalities in Two Variables

 

4. 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

4.4 Applications of Linear Systems

4.5 Solving Systems of Linear Inequalities

 

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 The Product Rule and Power Rules for Exponents

5.3 Multiplying Polynomials

5.4 Special Products

5.5 Integer Exponents and the Quotient Rule

5.6 Dividing a Polynomial by a Monomial

5.7 Dividing a Polynomial by a Polynomial

5.8 An Application of Exponents: Scientific Notation

 

6. Factoring and Applications

6.1 Factors; The Greatest Common Factor

6.2 Factoring Trinomials

6.3 Factoring Trinomials by Grouping

6.4 Factoring Trinomials by Using the FOIL Method

6.5 Special Factoring Techniques

6.6 Solving Quadratic Equations by Factoring

6.7 Applications of Quadratic Equations

 

7. 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

7.7 Applications of Rational Expressions

7.8 Variation

 

8. Roots and Radicals

8.1 Evaluating Roots

8.2 Multiplying, Dividing, and Simplifying Radicals

8.3 Adding and Subtracting Radicals

8.4 Rationalizing the Denominator

8.5 More Simplifying and Operations with Radicals

8.6 Solving Equations with Radicals

 

9. Quadratic Equations

9.1 Solving Quadratic Equations by the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations by the Quadratic Formula

9.4 Graphing Quadratic Equations

9.5 Introduction to Functions

Appendix: Inductive and Deductive Reasoning
Answers to Selected Exercises
Solutions to Selected Exercises
Index