can you help me reduce the following inequality (i need to get a relation between x and y -- express x in terms of y)
$\frac{n}{2x} < \frac{n}{(4+\epsilon)y}+1$
I would like to show somehow that $x > (1+\epsilon) y$ OR that $x>2y$
The assumption is that $0 < \epsilon < 1$ and that $n>4x, n>4y$, x and y are positive integers.
You already have what you want. For $x>0$, $y>0$, $\epsilon>0$, and $n>0$, you have: $$\dfrac{(4+\epsilon)}{n}\dfrac{n-2x}{2x}<y.$$ Hence:
$$y>\dfrac{a}{x}+b.$$ Where $a=\dfrac{4+\epsilon}{2}$ and $b=-\dfrac{4+\epsilon}{n}$