$$\begin{aligned}&x - \frac{x}{8} = \frac{7}{16}\\
&\frac{8x - x}{8} = \frac{7}{16}\\
&\frac{7x}{8} = \frac{7}{16}\\
&7x = \frac{7 \cdot 8}{16}\\
&7x = \frac{7}{2}\\
&x = \frac{7}{2} : 7\\
&x = \frac{7}{2} \cdot \frac{1}{7}\\
&x = \frac{1}{2}\\
&x = 0.5\end{aligned}$$
Ответ: $$\boxed{x = 0.5}$$