Elementary Algebra

Tom Carson’s first teaching experience was teaching guitar while an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study System. In addition to his work on the Carson Developmental Algebra Series, Tom also is the author of Prealgebra, Fourth Edition.   Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Bill has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In addition to his work on the Carson series, Bill is also the lead author of Integrated Algebra and Arithmetic, 2/e, also published by Pearson. In his spare time, he enjoys fishing, traveling, and hiking.

Preface

To the Student

Learning Styles Inventory

The Carson Math Study System

 

 

1. Foundations of Algebra

1.1 Number Sets and the Structure of Algebra

1.2 Fractions

1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers

1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers

1.5 Exponents, Roots, and Order of Operations

1.6 Translating Word Phrases to Expressions

1.7 Evaluating and Rewriting Expressions

            Summary and Review Exercises

            Practice Test

 

2. Solving Linear Equations and Inequalities

2.1 Equations, Formulas, and the Problem-Solving Process

2.2 The Addition Principle of Equality

2.3 The Multiplication Principle of Equality

2.4 Applying the Principles to Formulas

2.5 Translating Word Sentences to Equations

2.6 Ratios and Proportions

2.7 Percents

2.8 Solving Linear Inequalities

            Summary and Review Exercises

            Practice Test

            Chapters 1–2 Cumulative Review Exercises

 

3. Graphing Linear Equations and Inequalities

3.1 The Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Graphing Using Intercepts

3.4 Slope–Intercept Form

3.5 Point–Slope Form

3.6 Graphing Linear Inequalities

3.7 Introduction to Functions and Function Notation

            Summary and Review Exercises

            Practice Test

            Chapters 1–3 Cumulative Review Exercises

 

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations Graphically

4.2 Solving Systems of Linear Equations by Substitution; Applications

4.3 Solving Systems of Linear Equations by Elimination; Applications

4.4 More Applications with Systems of Equations

4.5 Solving Systems of Linear Inequalities

            Summary and Review Exercises

            Practice Test

            Chapters 1–4 Cumulative Review Exercises

 

5. Polynomials

5.1 Exponents and Scientific Notation

5.2 Introduction to Polynomials

5.3 Adding and Subtracting Polynomials

5.4 Exponent Rules and Multiplying Monomials

5.5 Multiplying Polynomials; Special Products

5.6 Exponent Rules and Dividing Polynomials

            Summary and Review Exercises

            Practice Test

            Chapters 1–5 Cumulative Review Exercises

 

6. Factoring

6.1 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, where a ≠ 1

6.4 Factoring Special Products

6.5 Strategies for Factoring

6.6 Solving Quadratic Equations by Factoring

6.7 Graphs of Quadratic Equations and Functions

            Summary and Review Exercises

            Practice Test

            Chapters 1–6 Cumulative Review Exercises

 

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Complex Rational Expressions

7.6 Solving Equations Containing Rational Expressions

7.7 Applications with Rational Expressions, Including Variation

            Summary and Review Exercises

            Practice Test

            Chapters 1–7 Cumulative Review Exercises

 

8. Roots and Radicals

8.1 Square Roots and Radical Expressions

8.2 Multiplying and Simplifying Square Roots

8.3 Dividing and Simplifying Square Roots

8.4 Addition, Subtraction, and Mixed Operations with Square Roots

8.5 Solving Radical Equations

8.6 Higher Roots and Rational Exponents

            Summary and Review Exercises

            Practice Test

            Chapters 1–8 Cumulative Review Exercises

 

9. Quadratic Equations

9.1 The Square Root Principle

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations Using the Quadratic Formula

9.4 Complex Numbers

9.5 Graphing Quadratic Equations

            Summary and Review Exercises

            Practice Test

            Chapters 1–9 Cumulative Review Exercises

 

Appendix: Mean, Median, and Mode

Photo Credits

Collaborative Exercises

Answers

Glossary

Index of Applications

Index