Then |-x+a|=-|x+a|

|x-a|+|x+a|=0

X-a=0，x+a=0。

This must be true for any X.

Obviously impossible.

If it is an even function

Then |-x+a|=|x+a|

So -x+a=x+a or-x+a =-x-a.

X=0 or a=0.

That is, when it holds for any x, it is a=0.

That is, a=0 is an even function, and not equal to 0 is a parity function.