More than one step
A multi-step equation needs several operations to isolate the variable. The strategy: undo operations in the reverse order of BEDMAS. Deal with addition and subtraction first, then multiplication and division.
Two-step equations
Example: 3x + 5 = 20
- Subtract 5: 3x = 15
- Divide by 3: x = 5
Check: 3(5) + 5 = 20 ✓
Example: x/4 − 2 = 6
- Add 2: x/4 = 8
- Multiply by 4: x = 32
Equations with brackets
Distribute first (or divide both sides if it’s simpler).
Example: 2(x + 3) = 18
- Method A: 2x + 6 = 18 → 2x = 12 → x = 6
- Method B: divide by 2 → x + 3 = 9 → x = 6
Combine like terms first
Example: 4x + 3 − x = 21
- Combine like terms: 3x + 3 = 21
- Subtract 3: 3x = 18
- Divide: x = 6
A general plan
| Step | Do |
|---|---|
| 1 | Distribute to remove brackets. |
| 2 | Combine like terms on each side. |
| 3 | Add or subtract to get the variable term alone. |
| 4 | Multiply or divide to get the variable alone. |
| 5 | Check in the original equation. |
Fractions
Multiply every term by the denominator to clear fractions.
Example: (x + 4)/3 = 5
- × 3: x + 4 = 15
- x = 11
Negative coefficients
Example: 10 − 2x = 4
- Subtract 10: −2x = −6
- Divide by −2: x = 3
Word problems
Problem: A phone plan costs $25 per month plus a $40 activation fee. After how many months will the total be $265?
- 25m + 40 = 265
- 25m = 225
- m = 9 months
Worked examples
Example 1: 5n − 7 = 18 → 5n = 25 → n = 5
Example 2: 3(2y − 1) = 21 → 6y − 3 = 21 → 6y = 24 → y = 4
Example 3: 7 + x/2 = 3 → x/2 = −4 → x = −8
Common mistakes
- Dividing before subtracting: for 3x + 5 = 20, dividing only 3x by 3 but not the 5 and 20.
- Distributing to only one term.
- Sign errors when moving terms.
- Skipping the check.
Try it yourself
- 4x − 9 = 15
- 2(a − 5) = 14
- 6 + 3k − k = 20
- (m − 2)/5 = 3
- 12 − 4p = 0
Answers: 1) 6 2) 12 3) 7 4) 17 5) 3
Quick recap
- Use inverse operations in reverse order.
- Distribute and combine like terms first.
- Check the solution in the original equation.