Rewrite without absolute value

Question

Rewrite without using the absolute value |-x+y| if x > y.

Answer 1

Recall that lAl = A if A > 0 and lA l= -A if A < 0.

If x > y, then x - y > 0. So, multiplying both sides by -1, we get -x + y < 0.

Therefore, l -x + y l = -(-x + y) = x - y