6. Решите уравнения: x + 3/5 = 4/7; x − 2/9 = 5/6; x · 3/8 = 5/12; x : 7/10 = 2/3; x + 3/5 = 3 1/10; x − 1 3/7 = 5/14; x · 2 2/3 = 8/9; x : 5/6 = 4 1/2.

1. \(x + \frac{3}{5} = \frac{4}{7}\). Вычтем \(\frac{3}{5}\): \(x = \frac{4}{7} - \frac{3}{5} = \frac{20}{35} - \frac{21}{35} = -\frac{1}{35}\).
2. \(x - \frac{2}{9} = \frac{5}{6}\). Прибавим \(\frac{2}{9}\): \(x = \frac{5}{6} + \frac{2}{9} = \frac{15}{18} + \frac{4}{18} = \frac{19}{18}\).
3. \(x \cdot \frac{3}{8} = \frac{5}{12}\). Разделим обе части на \(\frac{3}{8}\): \(x = \frac{5}{12} \cdot \frac{8}{3} = \frac{10}{9}\).
4. \(x : \frac{7}{10} = \frac{2}{3}\). Умножим обе части на \(\frac{7}{10}\): \(x = \frac{2}{3} \cdot \frac{7}{10} = \frac{7}{15}\).
5. \(x + \frac{3}{5} = 3\frac{1}{10}\). Вычтем \(\frac{3}{5}\): \(x = \frac{31}{10} - \frac{6}{10} = \frac{5}{2}\).
6. \(x - 1\frac{3}{7} = \frac{5}{14}\). Прибавим \(1\frac{3}{7} = \frac{10}{7}\): \(x = \frac{5}{14} + \frac{20}{14} = \frac{25}{14}\). Исправление: \(1\frac{3}{7} = \frac{10}{7} = \frac{20}{14}\), поэтому \(x = \frac{25}{14}\).
7. \(x \cdot 2\frac{2}{3} = \frac{8}{9}\). Так как \(2\frac{2}{3} = \frac{8}{3}\), то \(x = \frac{8}{9} : \frac{8}{3} = \frac{1}{3}\).
8. \(x : \frac{5}{6} = 4\frac{1}{2}\). Умножим обе части на \(\frac{5}{6}\): \(x = \frac{9}{2} \cdot \frac{5}{6} = \frac{15}{4}\).

Ответ: \(x = -\frac{1}{35}; \frac{19}{18}; \frac{10}{9}; \frac{7}{15}; \frac{5}{2}; \frac{25}{14}; \frac{1}{3}; \frac{15}{4}\) соответственно.