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LINEAR FUNCTIONS: SLOPE, GRAPHS AND MODELS
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Solving Inequalities
Solving Equations & Inequalities
Graph the rational function
Inequalities and Applications
Inequalities
Using MATLAB to Solve Linear Inequalities
Equations and Inequalities
Graph Linear Inequalities in Two Variables
Solving Equations & Inequalities
Teaching Inequalities:A Hypothetical Classroom Case
Graphing Linear Inequalities and Systems of Inequalities
Inequalities and Applications
Solving Inequalities
Quadratic Inequalities
Inequalities
Solving Systems of Linear Equations by Graphing
Systems of Equations and Inequalities
Graphing Linear Inequalities
Inequalities
Solving Inequalities
Solving Inequalities
Solving Equations Algebraically and Graphically
Graphing Linear Equations
Solving Linear Equations and Inequalities Practice Problems
Graphing Linear Inequalities
Equations and Inequalities
Solving Inequalities

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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
4. Signs (addition or subtraction) by using the addition principle (add opposites).
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.