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.
✗ The trap: x < −4.
✓ The fix: x > −4 (dividing by −2 flips the inequality).
How to actually fix it
- Highlight the inequality symbol before dividing by anything negative.
- Alternative: add 2x to both sides instead and never divide by a negative.
- Test one value from your answer region in the original inequality.
Made this mistake on a real question?
Practice Algebra questions here. Miss one and it is logged with the exact error, then brought back until you beat it.
Practice Algebra →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.