9.177. $216 x^{6}+19 x^{3}<1$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

9.177. $216 x^{6}+19 x^{3}<1$.
## Solution.

$216 x^{6}+19 x^{3}-1<0$. Solve the inequality as a quadratic equation with respect to

$$
x^{3},-\frac{1}{8}<x^{3}<\frac{1}{27} \Leftrightarrow-\frac{1}{2}<x<\frac{1}{3}
$$

Answer: $x \in\left(-\frac{1}{2} ; \frac{1}{3}\right)$.