Найдите корень уравнения: 3/4*(1/6*x-1/3)=2x-11 1/2.

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

\[\frac{1}{8}x - \frac{1}{4} = 2x - 11\frac{1^{\backslash 2}}{2}\]

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

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

\[- \frac{15}{8}x = - \frac{45}{4}\]

\[x = - \frac{45}{4}\ :\left( - \frac{15}{8} \right)\]

\[x = \frac{45}{4} \cdot \frac{8}{15} = 3 \cdot 2\]

\[x = 6.\]