Instructor's Solutions Manual for Algebra

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 participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student.

R. Prealgebra Review

    R.1 Factors and the Least Common Multiple

    R.2 Fractions

    R.3 Decimals and Percents

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

 

1. Real Numbers and Introduction to Algebra

    1.1 Study Skills Tips for Sucess in Mathematics

    1.2 Symbols and Sets of Numbers

    1.3 Expnents, 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

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

 

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 Linear Inequalities and Problem Solving

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

    

3. Graphing Equations and Inequalities

    3.1 Reading Graphs and the Rectangular Coordinate System

    3.2 Graphing Linear Equations

    3.3 Intercepts

    3.4 Slope and Rate of Change

Integrated Review - Summary on Solving Linear Equations

    3.5 Equations of Lines

    3.6 Graphing Linear Inequalities in Two Variables

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

4. Systems of Equations

    4.1 Solving Systems of Linear Equations by Graphing

    4.2 Solving Systems of Linear Equations by Substitution

Integrated Review - Summary on Solving Systems of Equations

    4.3 Solving Systems of Linear Equations by Addtion

    4.4 Systems of Linear Equations and Problem Solving

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

5. Exponents and Polynomials

    5.1 Exponents

    5.2 Negative Exponents and Scientific Notation

    5.3 Introduction to Polynomials

    5.5 Multiplying Polynomials

    5.6 Special Products

Integrated Review - Exponents and Operations on Polynomials

    5.7 Dividing Polynomials

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

6. Factoring Polynomials

    6.1 The Greatest Common Factor and Factoring by Grouping

    6.2 Factoring Trinomials of the Form x2 + bx + c

    6.3 Factoring Trinomials of the Form ax2 + bx + c

    6.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping

    6.5 Factoring by Special Products

Integrated Review - Choosing a Factoring Strategy 

    6.6 Solving Quadratic Equations and Problem Solving

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

7. Rational Expressions

    7.1 Simplifying Rational Expressions

    7.2 Multiplying and Dividing Rational Expressions

    7.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator

    7.4 Adding and Subtracting Rational Expressions with Different Denominators

    7.5 Solving Equations Containing Rational Expressions

Integrated Review - Summary on Rational Expressions

    7.6 Proportions and Problem Solving with Rational Equations

    7.7 Simplifying Complex Fractions

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

8. Graphs and Functions

    8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines

    8.2 Introduction to Functions

    8.3 Polynomial and Rational Functions

Integrated Review - Linear Equations in Two Variables and Functions

    8.4 Interval Notation, Finding Domains and Ranges from Graphs, and Graphing Piecewise-Defined Functions

    8.5 Shifting and Reflecting Graphs of Functions

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

9. Systems of Equations and Inequalities and Variation

    9.1 Solving Systems of Linear Equations in Three Variables and Problem Solving

    9.2 Solving Systems of Equations Using Matrices

Integrated Review - Systems of Linear Equations

    9.3 Systems of Linear Inequalities

    9.4 Variation and Problem Solving

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

10. Rational Exponents, Radicals, and Complex Numbers

   10.1 Radical Expressions and Radical Functions

    10.2 Rational Exponents

    10.3 Simplifying Radical Expressions

    10.4 Adding, Subtracting, and Multiplying Radical Expressions

    10.5 Rationalizing Numerators and Denominators of Radical Expressions

Integrated Review - Radicals and Rational Exponents

    10.6 Radical Equations and Problem Solving

    10.7 Complex Numbers

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

11. Quadratic Equations and Functions

    11.1 Solving Quadratic Equations by Completing the Square

    11.2 Solving Quadratic Equations by Using the Quadratic Formula

    11.3 Solving Equations by Using Quadratic Methods

Integrated Review - Summary on Solving Quadratic Equations

    11.4 Nonlinear Inequalities in One Variable

    11.5 Quadratic Functions and Their Graphs

    11.6 Further Graphing of Quadratic Functions

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

         

12. Exponential and Logarithmic Functions

    12.1 The Algebra of Functions

    12.2 Inverse Functions

    12.3 Exponential Functions

    12.4 Exponential Functions

    12.5 Logarithmic Functions

    12.6 Properties of Logarithms

Integrated Review - Functions and Properties of Logarithms 

    12.7 Common Logarithms, Natural Logarithms, and Change of Base

    12.8 Exponential and Logarithmic Equations and Problem Solving

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

13. Conic Sections

    13.1 The Parabola and the Circle

    13.2 The Ellipse and the Hyperbola

Integrated Review - Graphing Conic Sections

    13.3 Solving Nonlinear Systems of Equations

    13.4 Nonlinear Inequalities and Systems of Inequalities

        Group Activity

        Vocabulary Check

        Chapter Highlights

        Chapter Review

        Chapter Test

        Cumulative Review

 

Appendices

Appendix A: Transition Review: Exponents, Polynomials, and Factoring Strategies

Appendix B: Transition Review: Solving Linear and Quadratic Equations

Appendix C: Sets and Compound Inequalities

Appendix D: Absolute Value Equations and Inequalities

Appendix E: Determinants and Cramer’s Rule

Appendix F: Review of Angles, Lines, and Special Triangles

Appendix G: Stretching and Compressing Graphs of Absolute Value Functions

Appendix H: An Introduction to Using a Graphing Utility