Reverse Inequality

Question

If $|x|\leq 10$ and $|y|\leq 10$ and we want to find $||x|-|y||$

We can look at $||x|-|y||\leq |x|-|y|$

Where $|y|\leq 10\iff -10\leq y\leq 10$ so $10> -y >-10$

So we get $0 \leq x-y\leq 0$?

Answer 1

$-10 \le x \le 10$ combined with $-10 \le -y \le 10$ gives $-20 \le x-y \le 20$.