With a strong emphasis on skill-building, applications in the real world, and preparation for further math courses, this text unites the concepts of Elementary Algebra and Intermediate Algebra in one convenient and economical volume.
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 and Inequalities in Two Variables
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
3.6 Graphing Linear Inequalities in Two Variables
4 Polynomials and Exponents
4.1 Addition and Subtraction of Polynomials
4.2 Multiplication of Polynomials
4.3 Multiplication of Binomials
4.4 Special Products
4.5 Division of Polynomials
4.6 Nonnegative Integral Exponents
4.7 Negative Exponents and Scientific Notation
5 Factoring
5.1 Factoring Out Common Factors
5.2 Factoring the Special Products and Factoring by Grouping
5.3 Factoring ax2 + bx + c with a = 1
5.4 Factoring ax2 + bx + c with a 1
5.5 Factoring a Difference or Sum of Two Cubes
5.6 Solving Quadratic Equations by Factoring
6 Rational Expressions
6.1 Reducing Rational Expressions
6.2 Multiplication and Division
6.3 Finding the Least Common Denominator
6.4 Addition and Subtraction
6.5 Complex Fractions
6.6 Solving Equations with Rational Expressions
6.7 Applications of Ratios and Proportions
6.8 Applications of Rational Expressions
7 Systems of Linear Equations
7.1 Solving Systems by Graphing and Substitution
7.2 The Addition Method
7.3 Systems of Linear Equations in Three Variables
7.4 Solving Linear Systems Using Matrices
7.5 Determinants and Cramers Rule
8 More on Inequalities
8.1 Compound Inequalities in One Variable
8.2 Absolute Value Equations and Inequalities
8.3 Compound Inequalities in Two Variables
8.4 Linear Programming
9 Radicals and Rational Exponents
9.1 Radicals
9.2 Rational Exponents
9.3 Operations with Radicals
9.4 Quotients, Powers, and Rationalizing Denominators
9.5 Solving Equations with Radicals and Exponents
9.6 Complex Numbers
10 Quadratic Equations and Inequalities
10.1 Factoring and Completing the Square
10.2 The Quadratic Formula
10.3 Graphing Parabolas
10.4 More on Quadratic Equations
10.5 Quadratic and Rational Inequalities
11 Functions
11.1 Functions and Relations
11.2 Graphs of Functions and Relations
11.3 Transformations of Graphs
11.4 Graphs of Polynomial Functions
11.5 Graphs of Rational Functions
11.6 Combining Functions
11.7 Inverse Functions
12 Exponential and Logarithmic Functions
12.1 Exponential Functions and Their Applications
12.2 Logarithmic Functions and Their Applications
12.3 Properties of Logarithms
12.4 Solving Equations and Applications
13 Nonlinear Systems and the Conic Sections
13.1 Nonlinear Systems of Equations
13.2 The Parabola
13.3 The Circle
13.4 The Ellipse and Hyperbola
13.5 Second-Degree Inequalities
14 Sequences and Series
14.1 Sequences
14.2 Series
14.3 Arithmetic Sequences and Series
14.4 Geometric Sequences and Series
14.5 Binomial Expansions
A Diagnostic Test
B Chapters 1-6 Review
C Sets
D Geometry Review Exercises