I need some hints on how to solve this
$$\forall x\in\mathbb{R}\left(-|x|\le x\le |x|\right)$$
Hints: $$|x|=\max(x,-x) \tag1$$ $$-\max(a,b)=\min(-a,-b) \tag2$$
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Hints: $$|x|=\max(x,-x) \tag1$$ $$-\max(a,b)=\min(-a,-b) \tag2$$