Collect terms
Gather the unknown on one side and the numbers on the other.
AQA 8300 · A17 · Linear equations
Linear equations: undoing in reverse order
The inverse-operation mark. Each step is awarded for producing an equivalent equation, so an operation applied to one side only breaks the chain even if the final value is guessed correctly.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Inverse operation, both sides
Undo the last operation applied, performing it on both sides.
Solve and check
Reach the value and substitute it back into the original equation.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Applying an operation to one side only, or undoing the operations in the order they are written rather than in reverse order.
02
Why it survives revision
The working looks orderly, and every line individually looks like algebra. The error is a relationship BETWEEN two lines, not a mistake within one, and reading your own work line by line will never find it.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Undo the last operation that was applied first. Do it to both sides, and say which operation you are undoing.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form puts the unknown on both sides, so terms have to be collected before the reverse-order rule can even be applied.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: A17 · Linear equations. Inverse operations and exact equation states. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
What order do I undo operations in?
Reverse order. Undo the operation that was applied last first — so subtract before dividing, if the expression multiplied then added.
What if x is on both sides?
Collect the unknown onto whichever side keeps its coefficient positive, then solve as usual. Doing it the other way works too but invites a sign slip.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence