\[\boxed{\text{53\ (53).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ 5ax = - 45;\ \ x = 3\]
\[5 \cdot 3x = - 45\]
\[15a = - 45\]
\[a = - \frac{45}{15}\]
\[a = - 3\]
\[Ответ:\ при\ a = - 3.\]
\[2)\ (a - 4) \cdot x = - 5a + 4x - 7;\ \ \ \ \ \]
\[\ x = - 6\]
\[- 6 \cdot (a - 4) = - 5a - 24 - 7\]
\[- 6a + 24 = - 5a - 31\]
\[- 6a + 5a = - 31 - 24\]
\[- a = - 55\]
\[a = 55\]
\[Ответ:при\ a = 55.\]