This activity sheet, containing 20 exercises, focuses on solving equations that have variables on both sides of the equation.  It should follow lessons where students have solved one-step, two-step, and multi-step equations. 

The activity sheet begins with some guidelines for students to follow as the approach this new type of equations.

• Students are recommended to perform all distributive properties so each side on the equation only has terms that are either variables or constants.
• If the equations only have terms that contain variables or constants begin by trying to collect the variables on one side and the constants on the other side.
• Most students find it easier to work with an equation by avoiding negatives.  Although this isn’t totally possible, we can minimize the number of negative signs by moving the term that represents the small of two quantities.
• Students are reminded that when solving more complex equations they may run into an equation where no solutions are possible or all solutions are possible.

To help the students understand each guideline, examples are included for each recommendation. 
The activity sheet has
• Twelve exercises that resemble those in the guidelines,
• Six slightly more challenged equations with variables on both sides of the equation,
• One geometry-related problem where students have to write and solve their own equation with variables on both sides of the equation, and
• One challenging problem that deals with variables on both sides of the equal sign.

A set of solutions for all exercises is included. 

Activity-Sheet-on-Solving-Equations-with-Variables-on-Both-Sides