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# Basics

Basic Equations
 Sample Problem: x + 9 = 18 - 2x Solution: x = 3

Basic Proportions
 Sample Problem: ```4 8 - = -- x 20``` Solution: x = 10

Consecutive Integer Word Problems
 Sample Problem: What are two consecutive even integers that have a sum of 26? Solution: 12, 14

## Simplifying

Simplifying and Solving Equations with Multiple Signs
 Sample Problem: - -16 - x = 13 Solution: x = 3

Simplifying and Solving Equations by Combining Like Terms
 Sample Problem: 6x - 2 + 2x = -2 + 4x + 8 Solution: x = 2

## Multiplication

Two Single Terms
 Sample Problem: 11s * 12s3 Solution: 132s4

Distributive Property
 Sample Problem: 2(4 + 9x) Solution: 8 + 18x

FOIL Method
 Sample Problem: (1 + x)(3 + 2x) Solution: 3 + 5x + 2x2

## Exponents

Of Numbers
 Sample Problem: 52 Solution: 25

Of Variables
 Sample Problem: (k2m3)2 Solution: k4m6

Of Polynomials (Parentheses)
 Sample Problem: (2y + 9)2 Solution: 4y2 + 36y + 81

Order of Operations
 Sample Problem: 3 + 2 * 5x(y + 1) Solution: 3 + 10xy + 10x

## Negative Exponents

Negative Exponents of Numbers
 Sample Problem: 2-3 Solution: 1/8

Negative Exponents of Variables
 Sample Problem: j-3 Solution: 1/j3

Negative Exponents in Fractions
 Sample Problem: a-2b/a Solution: b/a3

## Substitution

Substitution Introduction
 Sample Problem: Evaluate: b + x2, where b = -2 and x = p + 1. Solution: p2 - 2p - 1

## Factoring

Factoring Numbers
 Sample Problem: 15 Solution: 1, 3, 5, 15

Finding a Greatest Common Factor (GCF) of Two Numbers
 Sample Problem: 42, 98 Solution: 14

Finding a Greatest Common Factor (GCF) of Two Terms
 Sample Problem: 21x2y, 7xy3 Solution: 3xy

Factoring a GCF From an Expression
 Sample Problem: 5x2 + 15x3 Solution: 5x2(1 + 3x)

Factoring a Difference Between Two Squares
 Sample Problem: x2 - 49 Solution: (x + 7)(x - 7)

Factoring a Trinomial
 Sample Problem: 5u2 + -11uv + 6v2 Solution: (5u - 6v)(u - v)

Factoring Completely
 Sample Problem: x4 + 7x3 + 12x2 Solution: x2(x + 3)(x + 4)

Solve By Factoring
 Sample Problem: x2 - 12x + 27 = 0 Solution: x = 3, 9

Completing the Square
 Sample Problem: x2 + x - 3.75 = 0 Solution: x = -2.5, 1.5

 Sample Problem: x2 + x - 3.75 = 0 Solution: x = -2.5, 1.5

## Graphing

Graphing Points
 Sample Problem: (1, 5), (-1, 3) Solution:

Reading the Coordinates of Points on a Graph
 Sample Problem: Solution: (3, 3)

Graphing Linear Equations by Graphing Two Points
 Sample Problem: y = 3x; points where x = -1 and x = 1 Solution:

Determining the Slope of a Line
 Sample Problem: Solution: slope: 1.5

Determining x and y Intercepts of a Line
 Sample Problem: Solution: y intercept: 1

Graphing Linear Equations Using Slope-Intercept Form
 Sample Problem: y = x + 2 Solution:

Determining a Linear Equation From the Graph of a Line
 Sample Problem: Solution: y = x + 1

Determining a Linear Equation From Two Points (Using the two-point formula)
 Sample Problem: (5, 13) and (10, 23) Solution: y = 2x + 3

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