Algebra A Combined Approach

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  • Edition: 4th
  • Format: Paperback
  • Copyright: 2011-02-09
  • Publisher: Pearson
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Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief.Algebra: A Combined Approach, Fourth Editionwas written to provide students with a solid foundation in algebra and help them effectively transition to their next mathematics course. The new edition offers new resources like theStudent Organizerand now includesStudent Resourcesin the back of the book to help students on their quest for success.

Author Biography

An award-winning instructor and best-selling 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 developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also pioneered the Chapter Test Prep Video to help students as they prepare for a test–their most “teachable moment!”


Elayn’s experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the videos useful for review.


Her textbooks and acclaimed video program support Elayn's passion of helping every student to succeed.

Table of Contents

Chapter R: Prealgebra Review                        

R.1 Factors and the Least Common Multiple

R.2 Fractions                                        

R.3 Decimals and Percents                                


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 Number                                

1.5 Subtracting Real Numbers                           

Integrated Review                                              

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                                              

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                                                                                   


Chapter 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                                              

3.5 Equations of Lines                                        

3.6 Graphing Linear Inequalities in Two Variables                                                                        


Chapter 4: Systems of Equations                                                                                                    

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 Addition                                 

Integrated Review                                              

4.4 Systems of Linear Equations and Problem Solving                                 


Chapter 5: Exponents and Polynomials          

5.1 Exponents                                                      

5.2 Negative Exponents and Scientific Notation

5.3 Introduction to Polynomials                       

5.4 Adding and Subtracting Polynomials       

5.5 Multiplying Polynomials                             

5.6 Special Products                                           

Integrated Review                                              

5.7 Dividing Polynomials


Chapter 6: Factoring Polynomials  

6.1 The Greatest Common Factor                     

6.2 Factoring Trinomials of the Form x 2 + bx + c

6.3 Factoring Trinomials of the Form ax 2 + bx + c

6.4 Factoring Trinomials of the Form ax 2 + bx + c  by coupling

6.5 Factoring by Special Products                    

Integrated Review                                              

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving


  Chapter 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                                              

7.6 Proportions and Problem Solving with Rational Equations                   

7.7 Simplifying Complex Fractions                                                                                   


Chapter 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                                              

8.4     Interval Notation, Finding Domains and Ranges from

Graphs and Graphing Piecewise-Defined Functions                                     

8.5 Shifting and Reflecting Graphs of Functions                           


Chapter 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

9.3 Systems of Linear Inequalities

Variation and Problem Solving


Chapter 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

10.6   Radical Equations and Problem Solving

10.7   Complex Numbers                                                                                                      


Chapter 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             

11.4   Nonlinear Inequalities in One Variable   

11.5   Quadratic Functions and Their Graphs  

11.6   Further Graphing of Quadratic Functions


Chapter 12: Exponential and Logarithmic Functions                                                 

12.1 The Algebra of Functions                         

12.2 Inverse Functions                                       

12.3 Exponential Functions                               

12.4 Exponential Growth and Decay Functions

12.5 Logarithmic Functions

Integrated Review                              

12.6 Properties of Logarithms                           

12.7 Common Logarithms, Natural Logarithms, and Change of Base         

12.8 Exponential and Logarithmic Equations and Problem Solving            


Chapter 13: Conic Sections                             

13.1 The Parabola and the Circle                      

13.2 The Ellipse and the Hyperbola 

Integrated Review              

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of Inequalities                                              



A Transition Review: Exponents, Polynomials, and Factoring Strategies

B. Transition Review: Solving Linear and Quadratic Equations

C.  Sets and Compound Inequalities

D.  Absolute Value Equations and Inequalities

E. Determinants and Cramer’s Rule

F. Review of Angles, Lines, and Special Triangles

G.  Stretching and Compressing Graphs of Absolute Value Functions

H. An Introduction to Using a Graphing Utility


Student Resources
Study Skills Builders

Bigger Picture Study Guide Outline

Practice Final Exam

Answers to Selected Exercises


Rewards Program

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