53. Решите уравнение: 1) \(10\frac{5}{8} - x = 7\frac{3}{5}\) 2) \((x - 2\frac{7}{8}) + 3\frac{5}{6} = 4\frac{2}{3}\)

Решение:

1. \( 10\frac{5}{8} - x = 7\frac{3}{5} \)
   \( x = 10\frac{5}{8} - 7\frac{3}{5} \)
   \( x = (10 - 7) + (\frac{5}{8} - \frac{3}{5}) \)
   \( x = 3 + \frac{5 \times 5 - 3 \times 8}{40} \)
   \( x = 3 + \frac{25 - 24}{40} \)
   \( x = 3\frac{1}{40} \)


2. \( (x - 2\frac{7}{8}) + 3\frac{5}{6} = 4\frac{2}{3} \)
   \( x - 2\frac{7}{8} = 4\frac{2}{3} - 3\frac{5}{6} \)
   \( x - 2\frac{7}{8} = (4-3) + (\frac{2}{3} - \frac{5}{6}) \)
   \( x - 2\frac{7}{8} = 1 + \frac{2 \times 2 - 5}{6} \)
   \( x - 2\frac{7}{8} = 1 + \frac{4 - 5}{6} \)
   \( x - 2\frac{7}{8} = 1 - \frac{1}{6} \)
   \( x - 2\frac{7}{8} = \frac{5}{6} \)
   \( x = \frac{5}{6} + 2\frac{7}{8} \)
   \( x = 2 + (\frac{5}{6} + \frac{7}{8}) \)
   \( x = 2 + \frac{5 \times 4 + 7 \times 3}{24} \)
   \( x = 2 + \frac{20 + 21}{24} \)
   \( x = 2 + \frac{41}{24} \)
   \( x = 2 + 1\frac{17}{24} \)
   \( x = 3\frac{17}{24} \)