I don't know where to start with proving this. Any help will be greatly appreciated.
2026-04-05 14:44:59.1775400299
How do I prove that $|x+y| \ge \big||x|-|y|\big|$?
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To prove that $|x+y| \geq ||x|-|y||$ is the same as to prove two separate inequalities: $|x+y| \geq |x| - |y|$ and $|x+y| \geq |y| - |x|$. Each of these two can be proved easily using the standard triangle inequality.