Equations and Inequalities: One–Step Inequalities

An inequality compares two expressions using an inequality sign.
-  Inequality signs are: “less than" , "greater than" , “less than or equal to” , and “greater than or equal to” .
-  You only need to perform one Math operation to solve the one-step inequalities.
-  To solve one-step inequalities, find the inverse (opposite) operation is being performed.
-  For dividing or multiplying both sides by negative numbers, flip the direction of the inequality sign.

Examples:
Example 1. Solve this inequality for .
Solution: The inverse (opposite) operation of addition is subtraction. In this inequality, 5 is added to . To isolate we need to subtract from both sides of the inequality.
Then: . The solution is:

Example 2. Solve the inequality.
Solution: is subtracted from . Add to both sides.


Example 3. Solve.
Solution: is multiplied to . Divide both sides by .
Then:

Example 4. Solve.
Solution: is multiplied to . Divide both sides by . Remember when dividing or multiplying both sides of an inequality by negative numbers, flip the direction of the inequality sign.
Then: