Вариант 1. Задание 5: Решите уравнение: 1) 8 7/9 - x = 3 5/6; 2) (x - 5/6) + 11/18 = 19/24

1) \(8 \frac{7}{9} - x = 3 \frac{5}{6}\) Чтобы решить уравнение, выразим x: \(x = 8 \frac{7}{9} - 3 \frac{5}{6}\) \(x = 8 + \frac{7}{9} - 3 - \frac{5}{6} = 5 + \frac{7 \cdot 2}{9 \cdot 2} - \frac{5 \cdot 3}{6 \cdot 3} = 5 + \frac{14}{18} - \frac{15}{18} = 5 - \frac{1}{18} = 4 \frac{17}{18}\) 2) \((x - \frac{5}{6}) + \frac{11}{18} = \frac{19}{24}\) \(x - \frac{5}{6} = \frac{19}{24} - \frac{11}{18}\) \(x - \frac{5}{6} = \frac{19 \cdot 3}{24 \cdot 3} - \frac{11 \cdot 4}{18 \cdot 4} = \frac{57}{72} - \frac{44}{72} = \frac{13}{72}\) \(x = \frac{13}{72} + \frac{5}{6}\) \(x = \frac{13}{72} + \frac{5 \cdot 12}{6 \cdot 12} = \frac{13}{72} + \frac{60}{72} = \frac{73}{72} = 1 \frac{1}{72}\)