Introductory Algebra

About our author Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most “teachable moment” (as they prepare for a test) along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Elayn is the author of 13 published textbooks and a new Interactive Assignment MyLab® Math course, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry. She has participated as an author across the broadest range of educational materials: textbooks, videos, tutorial software, and courseware. This provides an opportunity of various combinations for an integrated teaching and learning package offering great consistency for the student.

Chapter R. Prealgebra Review

R.1 Factors and the Least Common Multiple
R.2 Fractions
R.3 Decimals and Percents
R.4 Reading Pictographs and Bar, Line, and Circle Graphs


Chapter 1. Real Numbers and Introduction to Algebra

1.1 Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Exponents, Order of Operations, and Variable Expressions
1.4 Adding Real Numbers
1.5 Subtracting Real Numbers

Integrated Review – Operations on Real Numbers


1.6 Multiplying and Dividing Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying Expressions


Chapter 2. Equations, Inequalities, and Problem Solving

2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Further Solving Linear Equations

Integrated Review – Solving Linear Equations


2.4 An Introduction to Problem Solving
2.5 Formulas and Problem Solving
2.6 Percent and Mixture Problem Solving
2.7 Solving Linear Inequalities and Problem Solving


Chapter 3. Exponents and Polynomials

3.1 Exponents
3.2 Negative Exponents and Scientific Notation
3.3 Introduction to Polynomials
3.4 Adding and Subtracting Polynomials
3.5 Multiplying Polynomials
3.6 Special Products

Integrated Review – Exponents and Operations on Polynomials


3.7 Dividing Polynomials


Chapter 4. Factoring Polynomials

4.1 The Greatest Common Factor and Factoring by Grouping
4.2 Factoring Trinomials of the Form x2 bx + c
4.3 Factoring Trinomials of the Form ax2 + bx + c
4.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping
4.5 Factoring Perfect Square Trinomials and the Difference of Two Squares

Integrated Review – Choosing a Factoring Strategy


4.6 Solving Quadratic Equations by Factoring
4.7 Quadratic Equations and Problem Solving


Chapter 5. Rational Expressions

5.1 Simplifying Rational Expressions
5.2 Multiplying and Dividing Rational Expressions
5.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator
5.4 Adding and Subtracting Rational Expressions with Different Denominators
5.5 Solving Equations Containing Rational Expressions

Integrated Review – Summary on Rational Expressions


5.6 Proportions and Problem Solving with Rational Equations
5.7 Simplifying Complex Fractions


Chapter 6. Graphing Equations and Inequalities

6.1 The Rectangular Coordinate System
6.2 Graphing Linear Equations
6.3 Intercepts
6.4 Slope and Rate of Change
6.5 Equations of Lines

Integrated Review – Summary on Linear Equations


6.6 Introduction to Functions
6.7. Graphing Linear Inequalities in two Variables


Chapter 7. Systems of Equations

7.1 Solving systems of Linear Equations by Graphing
7.2 Solving Systems of Linear Equations by Substitution
7.3 Solving Systems of Linear Equations by Addition

Integrated Review – Systems of Linear Equations


7.4 Systems of Linear Equations and Problem Solving


Chapter 8. Roots and Radicals

8.1 Introduction to Radicals
8.2 Simplifying Radicals
8.3 Adding and Subtracting Radicals
8.4 Multiplying and Dividing Radicals

Integrated Review – Simplifying Radicals


8.5 Solving Equations Containing Radicals
8.6 Radical Equations and Problem Solving
8.7 Direct and Inverse Variation Including Radical Applications


Chapter 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

Integrated Review – Summary of Solving Quadratic Equations


9.4 Graphing Quadratic Equations in Two Variables



Appendices

A. Tables
B. Factoring Sums and Differences of Cubes
C. Mean, Median, Mode, Range, and Intro to Statistics
D. Sets
E. Review of Angles, Lines, and Special Triangles
F. Interval Notation and Finding Domains and Ranges from Graphs