53. Решите уравнение: 1) \(8\frac{5}{7} - x = 4\frac{9}{14}\) 2) \((x+7\frac{5}{8}) - 4\frac{13}{24} = 5\frac{1}{16}\)

Решение:

1. \( 8\frac{5}{7} - x = 4\frac{9}{14} \)
   \( x = 8\frac{5}{7} - 4\frac{9}{14} \)
   \( x = 8\frac{10}{14} - 4\frac{9}{14} \)
   \( x = 4\frac{1}{14} \)
2. \( (x+7\frac{5}{8}) - 4\frac{13}{24} = 5\frac{1}{16} \)
   \( x+7\frac{5}{8} = 5\frac{1}{16} + 4\frac{13}{24} \)
   \( x+7\frac{15}{24} = 5\frac{1}{16} + 4\frac{13}{24} \)
   \( x+7\frac{15}{24} = 5\frac{1}{16} + 4\frac{26}{48} \) - ошибка в исходных данных, приводим к общему знаменателю 48:
   \( x + 7\frac{15}{24} = 5\frac{3}{48} + 4\frac{26}{48} \)
   \( x + 7\frac{15}{24} = 9\frac{29}{48} \)
   \( x = 9\frac{29}{48} - 7\frac{15}{24} \)
   \( x = 9\frac{29}{48} - 7\frac{30}{48} \)
   \( x = 8\frac{77}{48} - 7\frac{30}{48} \)
   \( x = 1\frac{47}{48} \)

Ответ: 1) \(x = 4\frac{1}{14}\) 2) \(x = 1\frac{47}{48}\)