Calculus 1d?

Question

prove that | x - y | is greater than or equal to | x | - | y |.

Answer 1

This follows from the triangular inequlaity:
|x+y| <= |x| + |y|
write this as
|z+y| <= |z| + |y|
take z = x-y
then
z+y = x-y+y =x
|x| <= |x-y| +|y|
so
|x-y| >= |x| - |y|

Answer 2

read the link up to the inverse triangle inequality.