PEAZIT Aha card
Go straight to resources ↓Inequalities: negative division reverses the sign
Negative multiplication reverses order: 2 < 5 becomes −2 > −5. Division by a negative number also reverses the inequality.
| Expression | Meaning |
|---|---|
| −2x + 3 < 9 | Subtract 3 from both sides. |
| −2x < 6 | Divide by −2, so reverse the sign. |
| x > −3 | For example, x = 0 satisfies the original inequality. |
One worked example
- −2x + 3 < 9Subtract 3 from both sides.
- −2x < 6Divide by −2, so reverse the sign.
- x > −3For example, x = 0 satisfies the original inequality.
Watch out: Adding a negative number does not reverse the sign. Multiplying by an expression of unknown sign requires cases.
Goal, prerequisites and card origin
What you will learn: Solve a linear inequality involving division by a negative number.
What you need first: Number lines and linear equation operations.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Negative multiplication reverses order: 2 < 5 becomes −2 > −5. Division by a negative number also reverses the inequality.