53. Решите уравнение: 1) 10 5/8 - x = 7 3/5; 2) (x - 2 3/6) : 3/5 = 4 1/2.

Решение:

1. \(10\frac{5}{8} - x = 7\frac{3}{5}\)
2. \(x = 10\frac{5}{8} - 7\frac{3}{5} = \frac{85}{8} - \frac{38}{5} = \frac{85 \cdot 5 - 38 \cdot 8}{40} = \frac{425 - 304}{40} = \frac{121}{40} = 3\frac{1}{40}\)
3. \((x - 2\frac{3}{6}) : \frac{3}{5} = 4\frac{1}{2}\)
4. \(x - 2\frac{1}{2} = 4\frac{1}{2} \cdot \frac{3}{5}\)
5. \(x - \frac{5}{2} = \frac{9}{2} \cdot \frac{3}{5} = \frac{27}{10}\)
6. \(x = \frac{27}{10} + \frac{5}{2} = \frac{27}{10} + \frac{25}{10} = \frac{52}{10} = \frac{26}{5} = 5\frac{1}{5}\)

Ответ: 1) \(x = 3\frac{1}{40}\); 2) \(x = 5\frac{1}{5}\).