which are within the same interval is equal or less to the difference of the marginal values of the interval?
I have the following inequalities: $a \le x \le b$ $a \le y \le b$
How to prove that: $|x - y| \le b - a $
I tried subtracting y from the first inequality to get:
$a - y \le x - y \le b - y$ but don't know how to conclude: $| x - y | \le b - a$ ?