Question

How can I solve this: |n| ≥ n

Answer 1

$|n| \geq n$

For $n\leq 0$

$|n| \geq n \Leftrightarrow -n\geq n \Rightarrow 2n\leq0 \Rightarrow n\leq0$

For $n>0$

$|n| \geq n \Leftrightarrow n\geq n \Rightarrow 0\geq0\Rightarrow x\in\mathbb{R}$

$x>0 \vee x\leq 0 \Rightarrow \boxed{x\in\mathbb{R}}$

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$|n| \leq n$

For $n\leq0$

$|n|\leq n\Leftrightarrow -n\leq n \Rightarrow 2n\geq 0 \Rightarrow n\geq 0\\ n\geq 0 \wedge n\leq 0 \Rightarrow n=0$

For $n>0$

$|n|\leq n \Leftrightarrow n\leq n \Rightarrow 0 \leq 0\Rightarrow n\in \mathbb{R}\\ n\in \mathbb{R} \wedge n>0 \Rightarrow n>0$

$n>0 \vee n=0 \Rightarrow \boxed{x\geq0}$