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I'm working on a problem in which I have to find a range for r. I have an upper bound on it, but I can't seem to get the lower bound.

Here is the inequality to start with:

[tex]\lambda[/tex]r - r

^{3}+ [tex]\lambda[/tex] < 0

Eventually, I get it down to:

[tex]\lambda[/tex] < [tex]\frac{r^3}{r+1}[/tex]

However, I need r by itself on one side, and I have no idea what to do. Is there anything I actually could do or am I stuck?

Another note: r>0 and [tex]\lambda[/tex]>0. Thanks!