Step by Step
1
Solve the inequality like a normal equation
Use standard algebra steps — add, subtract, multiply, divide — to isolate the variable.
2
Watch for multiplying or dividing by a negative
Any time you multiply or divide both sides of an inequality by a negative number, the inequality sign must flip direction.
3
Flip the sign at that exact step
Greater-than becomes less-than (and vice versa) at the moment you divide or multiply by the negative — not before, not after.
4
Alternative: avoid the flip entirely
Instead of dividing by a negative, you can move the variable term to the other side of the inequality so its coefficient becomes positive — this avoids needing to flip the sign at all.
Applied Walkthrough
1
Solve −3x > 9. Dividing both sides by −3 requires flipping the inequality sign: x < −3.
2
Alternatively, avoid the flip: add 3x to both sides and subtract 9 from both sides instead: 0 > 3x + 9 becomes −9 > 3x.
3
Divide by positive 3 (no flip needed here since 3 is positive): −3 > x.
4
This is the same as x < −3 — both methods reach the identical answer; the second method just avoids ever dividing by a negative.
Exam Application
Exams test whether you remember to flip the inequality sign specifically when multiplying or dividing by a negative number, and whether you can recognize this is the single most commonly forgotten algebra rule.
⚠ Common Trap
The trap is forgetting to flip the sign, since this rule doesn't apply to addition or subtraction — only to multiplication or division by a negative number specifically. Many students flip the sign incorrectly for every step, or forget to flip it at all.
✓ Quick Self-Check
1. When do you flip an inequality sign?
When you multiply or divide both sides by a negative number.
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2. Solve −3x > 9.
x < −3.
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3. Do you flip the sign when adding or subtracting a negative number?
No — the flip rule only applies to multiplication or division by a negative, not addition or subtraction.
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4. What's an alternative strategy to avoid flipping the sign at all?
Move the variable term to the other side of the inequality so its coefficient becomes positive, avoiding division by a negative.
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5. What's the most common inequality mistake students make?
Forgetting to flip the sign when dividing or multiplying by a negative number.
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