The standard solving method
Inverse operations. Both sides. One step at a time.
Steps:
- Expand any brackets.
- Multiply through to clear fractions if convenient.
- Gather variable terms on ONE side.
- Gather constants on the OTHER side.
- Divide by the coefficient of the variable.
Example. .
- Expand: → .
- Add : .
- Divide: .
With unknown on both sides.
Move the variable terms to the side with the larger coefficient (keeps positive coefficient).
Example. .
- Subtract from both sides: .
- Subtract : .
- Divide: .
With fractions.
Multiply both sides by the LCM of the denominators to clear fractions.
Example. .
- LCM of is . Or: cross-multiply.
- .
- Expand: .
- Rearrange: , so .
Worked qualitative. Why move variable terms to the side with the larger coefficient?
- Keeps the coefficient positive.
- Less error-prone with sign mistakes.
- is cleaner than (but mathematically the same).
Edexcel tip. Show every step. Mark schemes credit each operation explicitly.
- Expand brackets first.
- Clear fractions by multiplying.
- Gather on one side.
- Divide by coefficient.