Flipping the inequality when dividing by a negative
Multiplying or dividing by a negative reverses the inequality.
The common mistake
Keeping the same sign after dividing by a negative: −2x > 6 becoming x > −3.
Instead: Any time you multiply or divide both sides by a negative number, flip < to > (or > to <).
Worked example with Guide me
Solve −2x > 6.
- Sugar · What do we divide by?Student · −2.
- Sugar · What happens to the sign?Student · It flips to <.
- Sugar · So?Student · x < −3.
Answer: x < −3. Check with x = −4: −2(−4) = 8 > 6.
Try 3 practice questions
1. Solve −3x ≤ 12.
Show answer
x ≥ −4
2. Solve 5 − x < 2.
Show answer
x > 3
3. Solve 4x > −8.
Show answer
x > −2 (no flip — dividing by a positive)
Quick answers
- What is the most common mistake with flipping the inequality when dividing by a negative?
- Keeping the same sign after dividing by a negative: −2x > 6 becoming x > −3.
- How do I get flipping the inequality when dividing by a negative right?
- Any time you multiply or divide both sides by a negative number, flip < to > (or > to <).
- Can you show a worked example?
- Solve −2x > 6. x < −3. Check with x = −4: −2(−4) = 8 > 6.
Related concepts
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Save this as a miss — practice it before your test