(1) Let x = 1. y = 3. z = -1. Then |x-y| = |x-z| = 2.
Let x = -1, y = 3, z = -1, then |x - y| = 4, |x - z| = 2.
Insufficient.

(2) Let x = -1, y = 3, z = -1, then |x - y| = 4, |x - z| = 2, then |x - y| > |x - z|
Let x = -1, y = z = 1, then |x - y| = |x - z|
Insufficient.

When combined,
Let x = -1, y = 3, z = -1, then |x - y| = 4, |x - z| = 2, then |x - y| > |x - z|
Let x = -2, y = -3, z = -1 then |x - y| = |x - z| = 1
Insufficient.

Then answer is E.

You may wonder how did I pick those numbers. The question asks is |x - y| > |x - z|. |x - y| represents the distance between x and y. |x - z| represents the distance between x and z.

Visualize the question by drawing a number line.

(1) |y - 0| > |z - 0| means the distance between y and 0 is greater than the distance between z and 0. Pick any y and z that satisfy this condition on the number line and move x around.

(2) x can be only left of 0 on the number line. Draw some scenarios for those.

Once you can visualize the problem on a number line, there is no need for algebra here.