# Solving Inequalities

I. Solving Inequalities

To solve an inequality, apply the equation solving techniques of: “Get rid of

1. Parentheses by using the distributive property.
2. Denominators: Multiply each side of equation by common denominator.
Decimals: Multiply each side of equation by 10, 100, 1000, etc.
3. Like terms on the same side by combining
Goal: The equation should be no more complicated than: 4x – 8 = -7x + 9
Get variable terms on one side of the equation and all constant terms on the other side.
Goal: The equation should be no more complicated than: 4x = -9
5. Coefficients by dividing by coefficient (BY SAME NUMBER). Goal: x = number

Two additional rules must be applied when solving an inequality:
1. When you multiply or divide an inequality by a negative number your must reverse the
inequality symbol.
2. The variable must be on the left.

Use these rules to solve the following inequalities:

You Try:

B. Three Forms of a Solution

Complete the following chart, remembering that < and > are represented by
parentheses while
≤ and ≥ are represented by brackets Interval is always expressed from LEFT to
RIGHT (smallest to largest value). And use the symbols ∞ and −∞ to represent infinity
and negative infinity.

 Solution Set Builder Notation Number Line Interval Notation

C. Determine whether the given number is a solution.

Solve the following inequalities and express the solution on a number line.