I'll step through each step. It would take a long time to explain all the rules that make this work, but hopefully an example will help. But basically you need to always do the same thing to both sides.

Problem: 0 > 1/3x - 2

(Add 2 to both sides, this will cancel the -2)

2 > 1/3 x

(Multiple both sides by 3, this will get rid of fraction)

6 > x

So you can use any number in the original formula that is greater than 6. So lets try 9 in the original formula.

0 > 1/3 (9) - 2

(Multiple 9 x 1/3 = 3)

0 > 3 - 2

(Subtract 2 from 3)

0 > -1

This is TRUE! Zero is greater than -1. So our test works.