Elementary and Intermediate Algebra

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Mark Dugopolski, Southeastern Louisiana University

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Chapter 1: Real Numbers and Their Properties
Section 1: The Real Numbers
Section 2: Fractions
Section 3: Addition and Subtraction of Real Numbers
Section 4: Multiplication and Division of Real Numbers
Section 5: Exponential Expressions and the Order of Operations
Section 6: Algebraic Expressions
Section 7: Properties of the Real Numbers
Section 8: Using the Properties to Simplify Expressions
Chapter 2: Linear Equations in One Variable
Section 1: The Addition and Multiplication Properties of Equality
Section 2: Solving General Linear Equations
Section 3: Identities, Conditional Equations, and Inconsistent Equations
Section 4: Formulas
Section 5: Translating Verbal Expressions into Algebraic Expressions
Section 6: Number, Geometric, and Uniform Motion Applications
Section 7: Discount, Investment, and Mixture Applications
Chapter 3: Inequalities in One Variable
Section 1: Inequalities
Section 2: Compound Inequalities
Section 3: Absolute Value Equations and Inequalities
Chapter 4: Linear Equations in Two Variables and Their Graphs
Section 1: Graphing Lines in the Coordinate Plane
Section 2: Slope
Section 3: Equations of Lines in Slope-Intercept and Standard Form
Section 4: The Point-Slope Form
Section 5: Applications of Linear Equations
Section 6: Introduction to Functions
Chapter 5: Polynomials and Exponents
Section 1: Addition and Subtraction of Polynomials
Section 2: Multiplication of Polynomials
Section 3: Multiplication of Binomials
Section 4: Special Products
Section 5: Division of Polynomials
Section 6: Positive Integral Exponents
Section 7: Negative Exponents and Scientific Notation
Chapter 6: Factoring
Section 1: Factoring Out Common Factors
Section 2: Factoring the Special Products and Factoring by Grouping
Section 3: Factoring ax2 + bx + c with a = 1
Section 4: Factoring ax2 + bx + c with a not equal to 1
Section 5: The Factoring Strategy
Section 6: Solving Quadratic Equations by Factoring
Chapter 7: Rational Expressions
Section 1: Reducing Rational Expressions
Section 2: Multiplication and Division
Section 3: Finding the Least Common Denominator
Section 4: Addition and Subtraction
Section 5: Complex Fractions
Section 6: Solving Equations with Rational Expressions
Section 7: Applications of Ratios and Proportions
Section 8: Applications of Rational Expressions
Chapter 8: Systems of Linear Equations and Inequalities
Section 1: Solving Systems by Graphing and Substitution
Section 2: The Addition Method
Section 3: Systems of Linear Equations in Three Variables
Section 4: Solving Linear Systems Using Matrices
Section 5: Determinants and Cramer's Rule
Section 6: Graphing Linear Inequalities in Two Variables
Section 7: Graphing Systems of Linear Inequalities
Section 8: Linear Programming
Chapter 9: Radicals and Rational Exponents
Section 1: Radicals
Section 2: Rational Exponents
Section 3: Operations with Radicals
Section 4: More Operations with Radicals
Section 5: Solving Equations with Radicals and Exponents
Section 6: Complex Numbers
Chapter 10: Quadratic Equations, Functions, and Inequalities
Section 1: Factoring and Completing the Square
Section 2: The Quadratic Formula
Section 3: Quadratic Functions and Their Graphs
Section 4: More on Quadratic Equations
Section 5: Quadratic and Rational Inequalities
Chapter 11: Functions
Section 1: Graphs of Functions and Relations
Section 2: Transformations of Graphs
Section 3: Combining Functions
Section 4: Inverse Functions
Section 5: Variation
Section 6: Synthetic Division and The Factor Theorem
Chapter 12: Exponential and Logarithmic Functions
Section 1: Exponential Functions and Their Applications
Section 2: Logarithmic Functions and Their Applications
Section 3: Properties of Logarithms
Section 4: Solving Equations and Applications
Chapter 13: Nonlinear Systems and the Conic Sections
Section 1: Nonlinear Systems of Equations
Section 2: The Parabola
Section 3: The Circle
Section 4: The Ellipse and Hyperbola
Section 5: Second-Degree Inequalities
Chapter 14: Sequences and Series
Section 1: Sequences
Section 2: Series
Section 3: Arithmetic Sequences and Series
Section 4: Geometric Sequences and Series
Section 5: Binomial Expansions

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