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# Inequality

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What interval consists of all u such that neither 2u nor 2u is in the interval (-1,1)?

May 13, 2022

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Neither 2u nor 2u doesn't make much sense to me. Please check if that is a typo.

Anyways, if u is a number such that 2u is not in the interval (-1, 1), that means $$2u \leq -1\text{ or }2u \geq 1$$. Solving each inequality gives $$u \leq -\dfrac12 \text{ or }u \geq \dfrac12$$. Then the answer is $$\left(-\infty, -\dfrac12\right] \cup \left[\dfrac12, \infty\right)$$

May 14, 2022