26. For what values of $x$ is the inequality

$$
\frac{4 x^{2}}{(1-\sqrt{1+2 x})^{2}}<2 x+9 ?
$$
26. The inequality makes sense for $x \geqslant-\frac{1}{2}$, but $x \neq 0$.

By getting rid of the denominator and the radical, we obtain the inequality $8 x^{3}-45 x^{2}<0$, from which $x<5 \frac{5}{8}$. Answer: $-\frac{1}{2} \leqslant x<0,0<x<5 \frac{5}{8}$.