Quick Inequality Question

I first accidentally posted this in Calculus & Beyond since it is for a 700-level class, but I'm realizing now that it's pretty basic, and it should probably go here:

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.

$$\lambda$$r - r3 + $$\lambda$$ < 0

Eventually, I get it down to:
$$\lambda$$ < $$\frac{r^3}{r+1}$$

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 $$\lambda$$>0. Thanks!

HallsofIvy
Homework Helper
I first accidentally posted this in Calculus & Beyond since it is for a 700-level class, but I'm realizing now that it's pretty basic, and it should probably go here:

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.

$$\lambda$$r - r3 + $$\lambda$$ < 0
$$\lambda$$ < $$\frac{r^3}{r+1}$$
Another note: r>0 and $$\lambda$$>0. Thanks!
You can't in any simple way. You can use the fact that points where one side is equal separate "<" from ">". However you still need to solve $r^3- \lamba r- \lambda= 0$. There is a "cubic formula" but it is very complicated.