Beginning Algebra

(Each chapter is followed by a Group Activity, Chapter Summary, Chapter Review Exercises, Chapter Test, and Cumulative Review Exercises [except Chapter 1]. The industry listed in the parentheses is the industry theme for that chapter)

1. The Real Number System.


Fractions.



Exponents, Order of Operations, and Inequality.



Variables, Expressions, and Equations.



Real Numbers and the Number Line.



Addition and Subtraction of Real Numbers.



Multiplication and Division of Real Numbers.



Properties of Real Numbers.



Simplifying Expressions.



2. Linear Equations and Inequalities in One Variable.


The Addition and Multiplication Properties of Equality.



More on Solving Linear Equations.



An Introduction to Applications of Linear Equations.



Formulas and Applications from Geometry.



Ratios and Proportions.



More About Problem Solving.



The Addition and Multiplication Properties of Inequality.



3. Linear Equations in Two Variables.


Linear Equations in Two Variables.



Graphing Linear Equations in Two Variables.



The Slope of a Line.



4. Polynomials and Exponents.


Addition and Subtraction of Polynomials; Graphing Simple Polynomials.



The Product Rule and Power Rules for Exponents.



Multiplication of Polynomials.



Special Products.



Integer Exponents and the Quotient Rule.



Division of Polynomials.



An Application of Exponents: Scientific Notation.



5. Factoring and Applications.


The Greatest Common Factor; Factoring by Grouping.



Factoring Trinomials.



More on Factoring Trinomials.



Special Factoring Rules.



Summary: Exercises on Factoring.



Solving Quadratic Equations by Factoring.



Applications of Quadratic Equations.



Solving Quadratic Inequalities.



6. Rational Expressions.


The Fundamental Property of Rational Expressions.



Multiplication and Division of Rational Expressions.



The Least Common Denominator.



Addition and Subtraction of Rational Expressions.



Complex Fractions.



Solving Equations Involving Rational Expressions.



Summary: Exercises on Operations and Equations with Rational Expressions.



Applications of Rational Expressions.



7. Equations of Lines, Inequalities, and Functions.


Equations of a Line.



Graphing Linear Inequalities in Two Variables.



Functions.



8. Linear Systems.


Solving Systems of Linear Equations by Graphing.



Solving Systems of Linear Equations by Substitution.



Solving Systems of Linear Equations by Elimination.



Applications of Linear Systems.



Solving Systems of Linear Inequalities.



9. Roots and Radicals.


Evaluating Roots.



Multiplication and Division of Radicals.



Addition and Subtraction of Radicals.



Rationalizing the Denominator.



Simplifying Radical Expressions.



Solving Equations with Radicals.



Fractional Exponents.



10. Quadratic Equations.


Solving Quadratic Equations by the Square Root Property.



Solving Quadratic Equations by Completing the Square.



Solving Quadratic Equations by the Quadratic Formula.



Summary: Exercises on Quadratic Equations.



Complex Numbers.



More on Graphing Quadratic Equations; Quadratic Functions.



Appendices.


Review of Decimals and Percents.



Sets.



Answers to Selected Exercises.


Index.


Index of Applications.