Equations and Inequalities: Multi–Step Inequalities

To solve a multi-step inequality, combine “like” terms on one side.
-  Bring variables to one side by adding or subtracting.
-  Isolate the variable.
-  Simplify using the inverse of addition or subtraction.
-  Simplify further by using the inverse of multiplication or division.
-  For dividing or multiplying both sides by negative numbers, flip the direction of the inequality sign.

Examples:
Example 1.  Solve this inequality. 
Solution: In this inequality, is subtracted from . The inverse of subtraction is addition. Add to both sides of the inequality:


Now, divide both sides by . Then:
The solution of this inequality is .

Example 2.  Solve this inequality. 
Solution: First, subtract from both sides:
Then simplify:
Now divide both sides by :

Example 3.  Solve this inequality.
Solution: First, subtract from both sides:


Divide both sides by . Remember that you need to flip the direction of inequality sign.