Multi-Step Equations: How to Solve
A multi-step equation usually requires more than one inverse operation before the variable is isolated. The goal is to get the variable alone on one side of the equation while keeping the equation balanced.
1) Simplify each side first
- Combine like terms if there are any on one side.
- Remove parentheses by distributing when needed.
- Clean up fractions or decimals if they appear.
2) Undo addition and subtraction
- Move constant terms away from the variable by using the opposite operation.
- Whatever you do to one side, do to the other side.
- Keep the variable terms together and the number terms together.
3) Undo multiplication and division
- If the variable is multiplied or divided by a number, use the opposite operation to isolate it.
- Be careful with negative numbers: a negative coefficient or divisor still works the same way, but signs must be handled carefully.
4) Check your solution
Substitute your answer back into the original equation. If both sides are equal, the solution is correct.
Helpful habit
Write each step clearly and simplify after every move. This reduces mistakes and makes it easier to spot errors if your answer does not check.