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Summary
Elementary Algebra is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems.
Table of Contents
1 Real Numbers and Their Properties
1.1 The Real Numbers
1.2 Fractions
1.3 Addition and Subtraction of Real Numbers
1.4 Multiplication and Division of Real Numbers
1.5 Exponential Expressions and the Order of Operations
1.6 Algebraic Expressions
1.7 Properties of the Real Numbers
1.8 Using the Properties to Simplify Expressions
2 Linear Equations and Inequalities in One Variable
2.1 The Addition and Multiplication Properties of Equality
2.2 Solving General Linear Equations
2.3 More Equations
2.4 Formulas
2.5 Translating Verbal Expressions into Algebraic Expressions
2.6 Number, Geometric, and Uniform Motion Applications
2.7 Discount, Investment, and Mixture Applications
2.8 Inequalities
2.9 Solving Inequalities and Applications
3 Linear Equations in Two Variables and Their Graphs
3.1 Graphing Lines in the Coordinate Plane
3.2 Slope
3.3 Equations of Lines in Slope-Intercept Form
3.4 The Point-Slope Form
3.5 Variation
4 Systems of Linear Equations and Inequalities
4.1 The Graphing Method
4.2 The Substitution Method
4.3 The Addition Method
4.4 Graphing Linear Inequalities in Two Variables
4.5 Graphing Systems of Linear Inequalities
5 Polynomials and Exponents
5.1 Addition and Subtraction of Polynomials
5.2 Multiplication of Polynomials
5.3 Multiplication of Binomials
5.4 Special Products
5.5 Division of Polynomials
5.6 Nonnegative Integral Exponents
5.7 Negative Exponents and Scientific Notation
6 Factoring
6.1 Factoring Out Common Factors
6.2 Factoring the Special Products and Factoring by Grouping
6.3 Factoring ax^2 + bx + c with a=1
6.4 Factoring ax^2 + bx + c with a not equal to 1
6.5 Factoring a Difference or Sum of Two Cubes
6.6 Solving Quadratic Equations by Factoring
7 Rational Expressions
7.1 Reducing Rational Expressions
7.2 Multiplication and Division
7.3 Finding the Least Common Denominator
7.4 Addition and Subtraction
7.5 Complex Fractions
7.6 Solving Equations with Rational Expressions
7.7 Applications of Ratios and Proportions
7.8 Applications of Rational Expressions
8 Powers and Roots
8.1 Roots, Radicals, and Rules
8.2 Simplifying Square Roots
8.3 Operations with Radicals
8.4 Solving Equations with Radicals and Exponents
8.5 Fractional Exponents
9 Quadratic Equations, Parabolas, and Functions
9.1 The Square Root Property and Factoring
9.2 Completing the Square
9.3 The Quadratic Formula
9.4 Applications of Quadratic Equations
9.5 Complex Numbers
9.6 Graphing Parabolas
9.7 Introduction to Functions
9.8 Combining Functions
Appendix A Geometry Review
Appendix B Table of Squares and Square Roots
Appendix C Common Logarithms
Appendix D Answers to Selected Exercises
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