Preserve the relation
Apply inverse operations exactly as for an equation, keeping the inequality sign.
AQA 8300 · A22 · Linear inequalities
Inequalities: the sign flips on a negative divide
The direction mark, and the boundary state. Dividing or multiplying by a negative reverses the relation, and a number line additionally has to encode whether the endpoint is included.
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.
Reverse on a negative
Reverse the relation at the moment of multiplying or dividing by a negative number.
Boundary and direction
Encode the answer on a number line with the correct open or closed endpoint and direction.
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
Keeping the inequality pointing the same way after dividing or multiplying by a negative number.
02
Why it survives revision
Every step before that one is identical to solving an equation, and the numerical boundary comes out correct — only the direction is wrong. Checking a value from the solution set would catch it instantly, and that check is almost never the habit.
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.
Reverse the relation at the moment of dividing or multiplying by a negative, then test one value from your answer.
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 asks for a number line or a list of integers, so the open or closed state of the boundary has to be right as well as the direction.
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: A22 · Linear inequalities. Preserve the relation through inverse operations, reverse it only after negative division, then encode the boundary and direction on a number line. 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.
When does the inequality sign flip?
Only when you multiply or divide both sides by a negative number. Adding or subtracting a negative does not flip it.
Open circle or closed circle?
Closed for ≤ and ≥, because the boundary value is included. Open for < and >, because it is not.
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