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How can I solve this: |n| ≥ n

I know it's infinite solutions, but why?

And also what about when |n| ≤ n
Why is it only zero and infinite positive solutions?

User Kevin Pope
by
7.7k points

1 Answer

7 votes


|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}}

-------------------------------------------------------------


|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}

User Casimir
by
8.3k points

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