College Algebra

2.

Equations and Inequalities

2.1.

Linear Equations in One Variable

2.1.1.

Structure of Linear Equations

2.1.2.

Basic Solving Techniques

2.1.2.1.

Addition and Subtraction Properties

2.1.2.2.

Multiplication and Division Properties

2.1.3.

Multi-Step Linear Equations

2.1.4.

Equations with Variables on Both Sides

2.1.5.

Equations with Fractions and Decimals

2.1.5.1.

Clearing Fractions

2.1.5.2.

Clearing Decimals

2.1.6.

Checking Solutions

2.1.7.

Identifying Special Cases

2.1.7.1.

Identity Equations

2.1.7.2.

Contradiction Equations

2.2.

Modeling with Linear Equations

2.2.1.

Translating Word Problems into Equations

2.2.2.

Setting Up and Solving Applications

2.2.3.

Number Problems

2.2.4.

Geometry Problems

2.2.5.

Mixture Problems

2.2.6.

2.2.6.1.

Distance and Time

2.2.6.2.

Work Rate Problems

2.2.7.

Money and Interest Problems

2.3.

Complex Numbers

2.3.1.

The Imaginary Unit i

2.3.1.1.

Definition and Notation

2.3.1.2.

2.3.1.3.

Simplifying Powers of i

2.3.2.

Standard Form of Complex Numbers

2.3.3.

Operations with Complex Numbers

2.3.3.1.

Addition and Subtraction

2.3.3.2.

2.3.3.3.

2.3.4.

Complex Conjugates

2.3.4.1.

Definition and Properties

2.3.4.2.

Using Conjugates for Division

2.3.5.

Graphing Complex Numbers

2.3.5.1.

2.3.5.2.

Absolute Value of Complex Numbers

2.4.

Quadratic Equations

2.4.1.

Standard Form of a Quadratic Equation

2.4.2.

Solving by Factoring

2.4.2.1.

Zero Product Property

2.4.2.2.

Factoring Techniques Review

2.4.3.

The Square Root Property

2.4.3.1.

Perfect Square Equations

2.4.3.2.

Completing the Square Method

2.4.4.

The Quadratic Formula

2.4.4.1.

Derivation of the Formula

2.4.4.2.

Using the Formula

2.4.4.3.

When to Use Each Method

2.4.5.

The Discriminant

2.4.5.1.

Calculating the Discriminant

2.4.5.2.

Nature of the Roots

2.4.5.3.

Real and Complex Solutions

2.4.6.

Applications of Quadratic Equations

2.4.6.1.

Projectile Motion

2.4.6.2.

Area and Geometry Problems

2.4.6.3.

Business Applications

2.5.

Other Types of Equations

2.5.1.

Polynomial Equations of Higher Degree

2.5.1.1.

Solving by Factoring

2.5.1.2.

Using Substitution

2.5.1.3.

Graphical Solutions

2.5.2.

Radical Equations

2.5.2.1.

Isolating the Radical

2.5.2.2.

Squaring Both Sides

2.5.2.3.

Multiple Radicals

2.5.2.4.

Checking for Extraneous Solutions

2.5.3.

Equations with Rational Exponents

2.5.3.1.

Converting to Radical Form

2.5.3.2.

Solving and Checking Solutions

2.5.4.

Equations in Quadratic Form

2.5.4.1.

Recognizing Quadratic Form

2.5.4.2.

Substitution Method

2.5.4.3.

Back-Substitution

2.5.5.

Absolute Value Equations

2.5.5.1.

Isolating the Absolute Value

2.5.5.2.

Setting Up Two Cases

2.5.5.3.

Checking Solutions

2.5.5.4.

No Solution Cases

2.6.

Linear Inequalities

2.6.1.

Properties of Inequalities

2.6.2.

Solving Linear Inequalities in One Variable

2.6.3.

Graphing Solutions on Number Line

2.6.4.

Interval Notation

2.6.5.

Set-Builder Notation

2.6.6.

Applications of Linear Inequalities

2.7.

Compound Inequalities

2.7.1.

Conjunction (And) Inequalities

2.7.2.

Disjunction (Or) Inequalities

2.7.3.

Solving and Graphing

2.7.4.

Writing Solutions in Various Forms

2.8.

Absolute Value Inequalities

2.8.1.

Less Than Cases

2.8.2.

Greater Than Cases

2.8.3.

Graphing Solutions

2.9.

Polynomial and Rational Inequalities

2.9.1.

Sign Chart Method

2.9.2.

Test Point Method

2.9.3.

Critical Points

2.9.4.

Solution Intervals

2.9.5.

Boundary Point Analysis

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1. Foundational Algebraic Concepts

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