Justify if True or False $\forall x\in\mathbb{R}\left(-|x|\le x\le |x|\right)$.

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$$\forall x\in\mathbb{R}\left(-|x|\le x\le |x|\right)$$

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Hints: $$|x|=\max(x,-x) \tag1$$ $$-\max(a,b)=\min(-a,-b) \tag2$$