Реши уравнение: 3/4*x-2/3*x+1=1/2*x+1/6.

\[\frac{3}{4}x - \frac{2}{3}x + 1 = \frac{1}{2}x + \frac{1}{6}\]

\[\frac{3}{4}x - \frac{2}{3}x - \frac{1}{2}x = \frac{1}{6} - 1^{\backslash 6}\]

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

\[- \frac{5}{12}x = - \frac{5}{6}\]

\[x = \frac{5}{6} \cdot \frac{12}{5}\]

\[x = \frac{12}{6}\]

\[x = 2.\]