Equations and Inequalities: Multi–Step Equations

To solve a multi-step equation, combine “like” terms on one side.
-  Bring variables to one side by adding or subtracting.
-  Simplify using the inverse of addition or subtraction.
-  Simplify further by using the inverse of multiplication or division.
-  Check your solution by plugging the value of the variable into the original equation.

Examples:
Example 1.  Solve this equation for .
Solution: First, bring variables to one side by adding to both sides. Then:
.
Simplify: . Now, subtract from both sides of the equation:

Divide both sides by :

Let’s check this solution by substituting the value of 2 for in the original equation:


The answer is correct.

Example 2.  Solve this equation for .
Solution: Subtract from both sides of the equation.

Divide both sides by , then:

Now, check the solution:


The answer is correct.