Question

Given the inequality -8 < 2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.

Answer 1

Start with -8 < 2.

- Multiplying or dividing by a positive number preserves the inequality direction.
- Multiply both sides by 2: (-8)·2 < 2·2 ⇒ -16 < 4 (still true).
- Divide both sides by 2: (-8)/2 < 2/2 ⇒ -4 < 1 (still true).

- Multiplying or dividing by a negative number reverses the inequality direction.
- Multiply both sides by -2: (-8)(-2) > 2(-2) ⇒ 16 > -4 (note the sign flipped).
- Divide both sides by -2: (-8)/(-2) > 2/(-2) ⇒ 4 > -1 (sign flipped again).

(You cannot multiply or divide both sides by 0.)