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For $x>0$, for which range of values of $\alpha$ is the following inequality true?
$x \log _{e}(x) \geq x-\alpha$

1. $\alpha \geq 1 / 2$
2. $\alpha \geq 0$
3. $\alpha \leq 2$
4. $\alpha \geq 1$
5. None of the above