I solved this question on number line, we can first analyze this eq |x-z| + |x| = |z|?

This equality is only possible, if x and z are on the same side of the number line.

(-) ----z----x----0--- or ---0-----x----z---- (+)

|distance between xandz| + |distance of x from origin| = |distance of z from origin|

given zy<xy<0 which can happen in two case.

z x y

- - + zy negative xy negative < both less than 0

+ + - zy negative xy negative < both less than 0

Therefore we don't even need option 1 and 2 to validate this |x-z| + |x| = |z|.

Answer : D

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Piyush K

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