Equations With Variables on Both Sides

Equations with Variables on Both Sides

When an equation has the variable on both sides, the goal is to gather all variable terms on one side and all constants on the other.

1) Choose a side for the variable

Pick the side that will be easiest to keep the variable on. Then use addition or subtraction to move the other variable terms across the equals sign.

2) Combine like terms

After moving terms, simplify each side separately. Combine variable terms and combine numbers.

3) Solve the simpler equation

Once there is only one variable term left, isolate the variable by undoing addition, subtraction, multiplication, or division.

4) Check your answer

Substitute your solution back into the original equation. Both sides should have the same value. If they do not, recheck your arithmetic and sign changes.

Helpful reminders

• Whatever you do to one side of an equation, do to the other side too.
• Be careful when moving a negative term.
• If the variable terms cancel and you get a true statement, there may be infinitely many solutions. If you get a false statement, there may be no solution.

A good final answer is simplified and verified by substitution.