53. Решите уравнение:

Решение:

1. \( 10\frac{5}{8} - x = 7\frac{3}{5} \)
   \( x = 10\frac{5}{8} - 7\frac{3}{5} = \frac{10 \cdot 8 + 5}{8} - \frac{7 \cdot 5 + 3}{5} = \frac{85}{8} - \frac{38}{5} = \frac{85 \cdot 5}{40} - \frac{38 \cdot 8}{40} = \frac{425 - 304}{40} = \frac{121}{40} = 3\frac{1}{40} \)
2. \( \left(x - 2\frac{7}{8}\right) + 3\frac{5}{6} = 4\frac{2}{3} \)
   \( x - 2\frac{7}{8} = 4\frac{2}{3} - 3\frac{5}{6} = \frac{4 \cdot 3 + 2}{3} - \frac{3 \cdot 6 + 5}{6} = \frac{14}{3} - \frac{23}{6} = \frac{14 \cdot 2}{6} - \frac{23}{6} = \frac{28 - 23}{6} = \frac{5}{6} \)
   \( x = \frac{5}{6} + 2\frac{7}{8} = \frac{5}{6} + \frac{2 \cdot 8 + 7}{8} = \frac{5}{6} + \frac{23}{8} = \frac{5 \cdot 4}{24} + \frac{23 \cdot 3}{24} = \frac{20 + 69}{24} = \frac{89}{24} = 3\frac{17}{24} \)

Ответ: 1) \( x = 3\frac{1}{40} \); 2) \( x = 3\frac{17}{24} \).