Найдите корень уравнения: 5/6*(1/3*x-1/5)=3x+3 1/3.

Ответ:

\[\frac{5}{6} \cdot \left( \frac{1}{3}x - \frac{1}{5} \right) = 3x + 3\frac{1}{3}\]

\[\frac{5 \cdot 1}{6 \cdot 3\ }x - \frac{8 \cdot 1}{6 \cdot 8} = 3x + \frac{10}{3}\]

\[\frac{5}{18}x - \frac{1}{6} = 3x + \frac{10}{3}\]

\[3x - \frac{5}{18}x = - \frac{1}{6} - \frac{20}{6}\]

\[2\frac{13}{18}x = - \frac{21}{6}\]

\[\frac{49}{18}x = - \frac{21}{6}\]

\[x = - \frac{21 \cdot 18}{6 \cdot 49} = - \frac{9}{7}\]

\[x = - 1\frac{2}{7}.\]