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Marge Lial 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.
Stan Salzman is a long time resident of Sacramento, California. Stan has taught at American River College for many years, where he was a member of the business department. He is the author of Business Math and Essential Math, published by Pearson Education, Inc., and is coauthor of Basic Math.
Diana Hestwood lives in Minnesota and has taught at Metropolitan Community College in Minneapolis for two decades. She has done research on the student brain and is an expert on study skills. She is the author of Lial/Hestwood’s Prealgebra and coauthor of Lial/Salzman/Hestwood’s Basic Math and Lial/Hestwood/Hornsby/McGinnis’s Prealgebra and Introductory Algebra.
R. Prealgebra Review
R.1 Fractions
R.2 Decimals and Percents
Study Skills: Using Your Math Textbook
Study Skills: Reading Your Math Textbook
1. 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: Tackling Your Homework
1.3 Real Numbers and the Number Line
Study Skills: Using Study Cards
1.4 Adding Real Numbers
1.5 Subtracting Real Numbers
1.6 Multiplying and Dividing Real Numbers
Summary Exercises Performing Operations with Real Numbers
1.7 Properties of Real Numbers
Study Skills: Reviewing a Chapter
1.8 Simplifying Expressions
Study Skills: Taking Math Tests
2. Equations, Inequalities, and Applications
2.1 The Addition Property of Equality
Study Skills: Managing Your Time
2.2 The Multiplication Property of Equality
Study Skills: Analyzing Your Test Results
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
3. Graphs of Linear Equations and Inequalities in Two Variables; Functions
3.1 Linear Equations in Two Variables; The Rectangular Coordinate System
Study Skills: Preparing for Your Math Final
3.2 Graphing Linear Equations in Two Variables
3.3 The Slope of a Line
3.4 Writing and Graphing Equations of Lines
Summary Exercises Applying Graphing and Equation-Writing Techniques for Lines
3.5 Graphing Linear Inequalities in Two Variables
3.6 Introduction to Relations and Functions
3.7 Function Notation and Linear Functions
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
Summary Exercises Applying Techniques for Solving Systems of Linear Equations
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
Summary Exercises Applying the Rules for Exponents
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 A General Approach to Factoring
6.7 Solving Quadratic Equations by Factoring
6.8 Applications of Quadratic Equations
7. Rational Expressions and Functions
7.1 Rational Expressions and Functions; Multiplying and Dividing
7.2 Adding and Subtracting Rational Expressions
7.3 Complex Fractions
7.4 Equations with Rational Expressions and Graphs
Summary Exercises Simplifying Rational Expressions vs Solving Rational Equations
7.5 Applications of Rational Expressions
7.6 Variation
8. Equations, Inequalities, and Systems Revisited
8.1 Review of Solving Linear Equations and Inequalities
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 Systems of Linear Equations in Two Variables
8.5 Systems of Linear Equations in Three Variables; Applications
9. Roots, Radicals, and Root Functions
9.1 Radical Expressions and Graphs
9.2 Rational Exponents
9.3 Simplifying Radical Expressions
9.4 Adding and Subtracting Radical Expressions
9.5 Multiplying and Dividing Radical Expressions
Summary Exercises Performing Operations with Radicals and Rational Exponents
9.6 Solving Equations with Radicals
9.7 Complex Numbers
10. Quadratic Equations, Inequalities, and Functions
10.1 Solving Quadratic Equations by the Square Root Property
10.2 Solving Quadratic Equations by Completing the Square
10.3 Solving Quadratic Equations by the Quadratic Formula
10.4 Equations Quadratic in Form
Summary Exercises Applying Methods for Solving Quadratic Equations
10.5 Formulas and Applications
10.6 Graphs of Quadratic Functions
10.7 More about Parabolas and Their Applications
10.8 Polynomial and Rational Inequalities
11. Inverse, Exponential, and Logarithmic Functions
11.1 Operations on Functions and Composition
11.2 Inverse Functions
11.3 Exponential Functions
11.4 Logarithmic Functions
11.5 Properties of Logarithms
11.6 Common and Natural Logarithms
11.7 Exponential and Logarithmic Equations and Their Applications
12. Nonlinear Functions, Conic Sections, and Nonlinear Systems
12.1 Additional Graphs of Functions; Operations and Composition
12.2 The Circle and the Ellipse
12.3 The Hyperbola and Other Functions Defined by Radicals
12.4 Nonlinear Systems of Equations
12.5 Second-Degree Inequalities and Systems of Inequalities