Inequality manipulation in two variables Given the inequality $m^4/s^5 - m \leq 2s^2$, the paper I am reading says that this implies that $s \geq 1/10\cdot m^{4/7}$. I tried manipulating the inequality to try and reproduce their result, but the best that I can get is $s \geq \sqrt[7]{m^4/(2+m)}$. Does anyone know how they managed to obtain their bound?
Edit: Both $s$ and $m$ are greater than or equal to $1$.

I've found a counterexample to the paper's deduction $s\geq\frac1{10}m^{4/7}$ for very small values of $s$ and $m$, namely $s=(1.158)10^{-24}$ and $m=10^{-40}$
Here are the wolframalpha evaluations: first inequality  evaluates to True, second inequality evaluates to False.
