I don't know how to solve this-> (-4e^-2x)-9sin3x>0.
Start by drawing the graphs of $\displaystyle \displaystyle \begin{align*} -4e^{-2x} \end{align*}$ and $\displaystyle \displaystyle \begin{align*} 9\sin{3x} \end{align*}$ and see where $\displaystyle \displaystyle \begin{align*} -4e^{-2x} > 9\sin{3x} \end{align*}$.