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svishal1123
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From the information that is given: |x|=y-z means
We have to consider 2 cases for x>0 and x<0.
If x>0 |x|=x and If x<0 |x|=-x
#1. x + y = z Hence we get, x = z - y. But we do not know if x>0 or x<0 so depending on that, if x>0 x=z-y else if x<0 -x=z-y and hence x=y-z
#2. x < 0 not sufficient since we do not have any information about y and z.
Combining #1 and #2 we can eliminate the case for x>0 and use x<0 and hence -x = z -y or x= y-z and hence confirm that C.) satisfies the question of |x|=y-z.
- Deepak
