Inequality Symbol

Aim: Why do we flip the inequality symbol when we multiply by a negative number?

When a number is divided by a negative number the inequality sign must be switched.

Example # 1:

-4x > 24
-4x > 24
-4      -4

x > -6
* Here is where the sign must be flipped 

Therefore the correct answer is x < -6


A way to visualize this is by remembering a number line

As you can see, the right side of 0, are all positive numbers, and on the left all numbers are positive.

If you look to the left side of -6, all the numbers are smaller than -6. Therefore, all numbers to the left side of -6 make the statement true.