Algebra, analysis and inequality signs involving modulus signs

Question

How do you derive that | |x|-|y| |<= |x-y|

This is known as the reverse triangle inequality, see here. – user780985 May 02 '20 at 02:29 — user780985, May 02 '20 at 02:29

score 1 · Accepted Answer · answered May 02 '20 at 03:30

1

If you already have the triangle inequality -

$$ |x| = |x-y+y| \leq |x-y| + |y|. $$

Subtract from both sides to conclude that

$$ |x| - |y| \leq |x-y|. $$

answered May 02 '20 at 03:30

Moon Bears-C-

1 Answers1