i need help in proving this essential ineuality which i don't know how to prove (quite trivial isn't it):(adsbygoogle = window.adsbygoogle || []).push({});

||x|-|y||<=|x-y|

i know that my first trick is this:

|x|=|(x-y)+y|<=|(x-y)|+|y|

|x|-|y|<=|x-y|

and iv'e been told to do so also with |y| and i get to this:

|y|-|x|<=|y-x|

and then adding both inequalities give us with this:

|x-y|>=-|y-x|

here i'm pretty much puzzled, so can you help, or add some insight or hints.

btw, i'm in a hurry so if i have angried anyone by posting here, sorry!

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# Triangle ineuality, in need for help.

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