\[\boxed{\text{269\ (269).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{1}{8} < x < \frac{1}{7}\ \ \ \ \ \ \ \ | \cdot 2\]
\[\frac{2}{16} < x < \frac{2}{14}\]
\[x = \frac{2}{15}.\]
\[\textbf{б)}\ \frac{1}{6} < x < \frac{1}{5}\ \ \ \ \ \ \ \ | \cdot 3\]
\[\frac{3}{18} < x < \frac{3}{15}\]
\[x = \frac{3}{16}.\]