How to write this math rule using latex ?

[BGAmodzX]

Hello everyone.

I have a mathematical rule about absolute value am trying to write in latex so that is better expressed for the mathematician and actually try to solve it.

Here it is :
1) It is known that : IxI = x if x >= 0
2) And : IxI = -x if x < 0

3 ) So as a result it goes from it that for every x we have x =< IxI

Question to solve :

Prove 3)

Note : Just give some hints and ill try to elaborate a solution