Решите уравнение: 3/4*(1/6*x-1/3)=3x-11 1/2.

\[\frac{3}{4} \cdot \left( \frac{1}{6}x - \frac{1}{3} \right) = 3x - 11\frac{1}{2}\]

\[\frac{1}{8}x - \frac{1}{4} = 3x - \frac{23}{2}\]

\[2\frac{7}{8}x = 11\frac{1}{4}\]

\[x = \frac{45 \cdot 8}{4 \cdot 23} = \frac{45 \cdot 2}{1 \cdot 23} = \frac{90}{23}\]

\[x = 3\frac{21}{23}\]

\[Ответ:x = 3\frac{21}{23}\text{.\ }\]