Algebra
Single-variable equations
Multi-step equations
20 practice questions
2 video lessons
Theory + worked examples
Theory
A multi-step equation needs several moves. Work in order:
- Distribute to clear parentheses.
- Combine like terms on each side.
- Move variables to one side, constants to the other.
- Undo with inverse operations.
Simplify each side first, then isolate the variable.
The order for a multi-step equation.
Variables on both sides.
General strategy:
\[\text{simplify each side}\ \to\ \text{collect variables}\ \to\ \text{isolate}\]
Move the smaller variable term to avoid negatives.
How to solve multi-step equations
- Distribute across parentheses.
- Combine like terms.
- Add/subtract to gather variables on one side.
- Divide to isolate the variable, then check.
Example 1 — Two steps
Solve \(2x+3=11\).
Solution
Undo addition, then multiplication.
| \(2x\) | \(=\) | \(8\) |
| \(x\) | \(=\) | \(4\) |
Example 2 — Distribute first
Solve \(3(x-2)=12\).
Solution
Distribute, then solve.
| \(3x-6\) | \(=\) | \(12\) |
| \(3x\) | \(=\) | \(18\) |
| \(x\) | \(=\) | \(6\) |
Example 3 — Variables on both sides
Solve \(5x-3=2x+9\).
Solution
Collect variables on one side.
| \(3x-3\) | \(=\) | \(9\) |
| \(3x\) | \(=\) | \(12\) |
| \(x\) | \(=\) | \(4\) |
Example 4 — Combine then solve
Solve \(2(x+1)+3x=17\).
Solution
Distribute, combine, solve.
| \(2x+2+3x\) | \(=\) | \(17\) |
| \(5x+2\) | \(=\) | \(17\) |
| \(x\) | \(=\) | \(3\) |
Common pitfalls
Distribute to every term inside parentheses.
Do the same to both sides at every step.
Combine like terms before isolating.
Frequently asked questions
What is a multi-step equation?
An equation needing more than one operation to solve.
What do you do first?
Distribute and combine like terms.
How do you handle variables on both sides?
Add or subtract to gather them on one side.
Should you still check?
Yes — substitute your answer back.
More in Single-variable equations