Question

$$\{ x e z : x ^ { 2 } \gt 9 x ^ { 3 } \leq 130 \}$$

Solve for x

$\left\{\begin{matrix}x<-\frac{\sqrt{3}\sqrt[4]{ez}}{3}\text{, }&z\geq 0\\x\in (0,\frac{\sqrt[3]{390}}{3}]\text{, }&z>\frac{152100^{\frac{2}{3}}}{9e}\\x\in (0,\frac{\sqrt{3}\sqrt[4]{ez}}{3})\text{, }&z>0\text{ and }z\leq \frac{152100^{\frac{2}{3}}}{9e}\\x<0\text{, }&z<0\end{matrix}\right.$

Solve for z

$\left\{\begin{matrix}z>\frac{9x^{4}}{e}\text{, }&x>0\text{ and }x\leq \frac{\sqrt[3]{390}}{3}\\z<\frac{9x^{4}}{e}\text{, }&x<0\end{matrix}\right.$