Question

Consider the inequality −6z<24.

Solve the inequality. Explain and determine if the inequality symbol is reversed.

Answer 1

Answer: z > -4

Reason: Divide both sides by -6 to isolate z. The inequality symbol does reverse or flip. This happens any time you multiply or divide both sides by a negative number.

Here's another approach that takes a slightly longer route:

-6z < 24

-6z+6z < 24+6z

0 < 24+6z

0-24 < 24+6z-24

-24 < 6z

6z > -24

6z/6 > -24/6

z > -4

The sign flip does not happen if you divide both sides by a positive number.

But notice the sign flip happened when going from -24 < 6z to 6z > -24