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: $$| x - y | \le b - a$$ ?