I missed this question because I made a wrong assumption; please clarify.

Is |x| = y - z ?

(1) x + y = z
(2) x < 0

my approach:
If actually |x| = y-z
then x = y-z.................subject to x>0
OR x = z-y....................subject to x <0
my assumption is that, the question is asking for the sign of x.

(1) this implies that x < 0, isn't it? ....
(2) x<0.....meaning x=z-y....just as in (1)
I picked D as my answer.
Please correct me.