dreamv wrote:If zy<xy<0, is |x-z|+|x|=|z|?

1) z<x
2) y>0

zy < xy < 0

Case 1: If y < 0, then z > x > 0
z > x implies |x - z| = -(x - z) = z - x, since both x and z > 0
This means |x| = x and |z| = z
So, |x - z| + |x| = z - x + x = z
Hence, |x - z| + |x| = |z| is true.

Case 2: If y > 0, then z < x < 0
z < x implies |x - z| = x - z, since both x and z < 0
This means |x| = -x and |z| = -z
So, |x - z| + |x| = x - z - x = -z
Hence, |x - z| + |x| = |z| is true.

From both the cases, we can conclude that |x - z| + |x| = |z| is true. But we could conclude the answer without using either statement. Statements 1 and 2 are given in the question itself. What is the source of this question?