$x+y\ge x+y$
Can I write this? Even though the left side will never be bigger than the right side is this inequality true? Got something similar on another task and wanted to know if I could write this as an answer.
$|a-b|\ge ||a|-|b||$ my task is to prove this by using the triangle inequality on $a=a-b+b$ and I've got to this point $|a-b|\ge |a|-|b|$ and I was also wondering if I could take the absolute value on both sides of the inequality to get to the other inequality.