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

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

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

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

\[3\frac{7}{9}x = \frac{- 1 \cdot 2 - 5 \cdot 3}{6}\]

\[3\frac{7}{9}x = \frac{- 2 - 15}{6}\]

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

\[x = - \frac{17 \cdot 9}{6 \cdot 34} = - \frac{1 \cdot 3}{2 \cdot 2}\]

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

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