№ 2. Решите уравнение: а) (2/3)x + 3 2/5 = 4 2/3; б) x : 1 1/6 = 3 3/7 : 6 2/3.

а)

\(\frac{2}{3}x + 3\frac{2}{5} = 4\frac{2}{3}\).

\(\frac{2}{3}x = 4\frac{2}{3} - 3\frac{2}{5} = \frac{14}{3} - \frac{17}{5} = \frac{70-51}{15} = \frac{19}{15}\).

\(x = \frac{19}{15} : \frac{2}{3} = \frac{19}{15} \cdot \frac{3}{2} = \frac{19}{10} = 1\frac{9}{10}\).

б)

\(x : 1\frac{1}{6} = 3\frac{3}{7} : 6\frac{2}{3}\).

\(x = 1\frac{1}{6} \cdot \left(3\frac{3}{7} : 6\frac{2}{3}\right)\).

\(x = \frac{7}{6} \cdot \left(\frac{24}{7} : \frac{20}{3}\right) = \frac{7}{6} \cdot \frac{24}{7} \cdot \frac{3}{20} = \frac{3}{5}\).

Ответ: а) \(x=1\frac{9}{10}\); б) \(x=\frac{3}{5}\).