-x < x 

find a counterexample.

x = 0 is a counterexample because -0 < 0 is the same as 0 < 0 which says something
can be less than itself, which is false, so 0 is, in fact, the largest possible
counterexample.

-x < x
-0 < 0
 0 < 0     <--nothing can be less that itself!

x = -1 is a counterexample because -(-1) is the same as 1, which also says something 
can be less than itself.

   -x < x
-(-1) < 1
    1 < 1   <--nothing can be less than itself. 

-x < x is always true for positive numbers and is always false for zero and
negative numbers.

Edwin