Solve Equations with Variables on Both Sides

In this lesson, you will learn to solve equations that have variables on both sides. There are many real world problems that can be solved by this type of equation. To solve this type of equation, you will have to get the terms with variables on one side of the equal sign. Once again, the goal is to isolate the variable on one side of the equation. It is very important in this type of equation that you show each step in the solution to avoid confusion. Are you ready to get started?

Example 1:   Remember – group the terms with variables on one side of the equation and simplify.

day 88.1

Check your solution: 60 – 3(5) = 9(5); 60 – 15 = 45

Example 2:   It works with negative numbers, too!

day 88.2

Check your solution: -4(36) + 72 = -2(36); -144 + 72 = -72


day 88.3

Jane enjoys playing tennis and wants to join a Tennis Club. Members at the Daves Creek Tennis Club pay $250 plus $5 per visit to play at the indoor courts. Non-members must pay $15 per visit. How many visits must a member make to the courts for it to cost her the same as non-paying members?


Summarize the problem, using only key words or phrases and rewrite the problem as a statement.

Jane will pay the same amount as a member or non-member after v trips to the tennis court.

Now, translate this information into an equation with variables on both sides and solve.

day 88.4

Interpret the solution: If Jane joins the Tennis Club, she will have to visit the indoor tennis court 25 times for it to cost the same as a non-member.