• anonymous
im trying to prove the inverse triangle inequality$||x|-|y||\leq|x-y|$like this:$x=x-y+y,$$|x|=|x-y+y|,$$|x|\leq|x-y|+|y|,$$|x|-|y|\leq|x-y|.$i get stuck here; dont know if its legit or not to take the absolute value of the LHS and preserve the inequality. help?
Mathematics

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