An easy way to approach this ineq will be to analyze that:
|x-z| + |x| = |z| means
|z-x| = |z| - |x|.
|z-x| is the distance between z and x on number line. It can only be equal to |z| - |x| if both z and x have the same signs.
a) z < x - implies that y > 0 because zy < xy.
If y > 0 then z < x < 0. Therefore both have same signs.
b) y>0 then z < x < 0. Therefore both have same signs.
D is the answer i think
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