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

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

\[\frac{2}{9}x - \frac{1}{3} = 4\ x + \frac{5}{2}\]

\[\frac{36}{9}x - \frac{2}{9}x = - \frac{2}{6} - \frac{15}{6}\]

\[\frac{34}{9}x = - \frac{17}{6}\]

\[x = - \frac{17 \cdot 9}{6 \cdot 34}\]

\[x = - \frac{3}{4}.\]