If you multiply or divide an inequality by a negative number what happens to the inequality sign?

opposite the direction of sign

The inequality sign will change to the opposite. For example, < will change to >.

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

In the following example, notice how the < sign becomes a > sign when the inequality is divided by -2

-2x - 10 < 2

-2x - 10 + 10 < 2 + 10

-2x < 12

x > -6 [Dividing by -2 required the flipping of the inequality sign]

The inequality sign will flip around.

For example:

5x > -3

If you multiply or divide one side by -1 then the sign will flip around so it will become:

-5x < 3

When applying a negative value to an inequality a MAIN rule to note : Swap inequality sign opposite direction when applying a negative value