Absolute value proof with epsilon

Question

I'm having trouble with this proof. any hints would be greatly appreciated!

If $x$ is a positive real number, show that for some $\epsilon$ $>0, $ then $y\in \Bbb{R}$ is positive if $|(x-y)|< $ $\epsilon$.

Answer 1

Hints:

All the $y$ satisfies $|x-y|<\epsilon$ is the set $(x-\epsilon, x+\epsilon)$

Answer 2

Hins. Take: $$\epsilon=x$$. then got that $y>0$