1. Show that for all real numbers x and y:
a) |x-y| ≤ |x| + |y|
Possibly -|x| ≤ x ≤ |x|,
and -|y| ≤ y ≤ |y|?
The Attempt at a Solution
I tried using a direct proof here, but I keep getting stuck, especially since this is my first time ever coming across mathematical analysis, so I don't have much intuition for it. What I did think was possibly trying to use the triangle inequality somehow?
So far I have added the two above equations together to get
-|x| - |y| ≤ x + y ≤ |x| + |y|
But If that is right then I have no idea how to manipulate it to get the original statement to be proven. Any help would be much appreciated as I seem to keep going in circles.