\[\boxed{\text{1040.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\textbf{а)}\ \frac{a - 1}{4} - 1 > \frac{a + 1}{3} + 8\]
\[\frac{a - 1 - 4}{4} > \frac{a + 1 + 24}{3}\]
\[3 \cdot (a - 5) > 4 \cdot (a + 25)\]
\[3a - 15 > 4a + 100\]
\[- a > 115\ \ \ | \cdot ( - 1)\]
\[a < - 115 \Longrightarrow \ \ a \in ( - \infty;\ - 115)\]
\[\textbf{б)}\ \frac{3a - 1}{2} - \frac{a - 1}{4} > 0\]
\[\frac{6a - 2 - a + 1}{2} > 0\]
\[5a - 1 > 0\]
\[5a > 1\]
\[a > 0,2 \Longrightarrow \ a \in (0,2;\ + \infty)\]
\[\textbf{в)}\ \frac{1 - 2a}{4} - 2 < \frac{1 - 5a}{8}\]
\[\frac{1 - 2a - 8}{4} < \frac{1 - 5a}{8}\]
\[- 4a - 14 < 1 - 5a\]
\[a < 15 \Longrightarrow \ \ a \in ( - \infty;15)\]
\[\textbf{г)}\frac{5a}{6} - \frac{3a - 1}{3} +\]
\[+ \frac{2a - 1}{2} < 1\ \ \ \ | \cdot 6\]
\[5a - 2 \cdot (3a - 1) +\]
\[+ 3 \cdot (2a - 1) < 6\]
\[5a - 6a + 2 + 6a - 3 - 6 < 0\]
\[5a < 7\ \ \ |\ :5\]
\[a < \frac{7}{5}\]
\[a < 1,4 \Longrightarrow \ \ a \in ( - \infty;1,4)\]