Forgetting to flip the inequality when dividing by a negative
−2x < 8 becomes x < −4 if you divide and forget to flip — and x > −4 is what's actually true.
Why it happens
Flipping feels like an arbitrary bolt-on rule, so it drops out first under pressure. (It isn't arbitrary: multiplying by a negative reverses the number line.)
See the trap
Solve −2x < 8.
x < −4.
x > −4 (dividing by −2 flips the inequality).
How to actually fix it
- 1Highlight the inequality symbol before dividing by anything negative.
- 2Alternative: add 2x to both sides instead and never divide by a negative.
- 3Test one value from your answer region in the original inequality.
Practice this trap · 2 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
Does adding a negative flip it too?
No — only multiplying or dividing by a negative flips the direction. Adding/subtracting never does.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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