222. Решите уравнение: а) 8/11 - z = 3 9/11; б) y - 4 3/5 = 2 4/5; в) 8 16/27 - (x - 2 17/27) = 5 8/27

Решение:

1. а) \( \frac{8}{11} - z = 3\frac{9}{11} \)
   \( z = \frac{8}{11} - 3\frac{9}{11} \)
   \( z = \frac{8}{11} - \frac{3 \cdot 11 + 9}{11} = \frac{8}{11} - \frac{42}{11} = \frac{8 - 42}{11} = -\frac{34}{11} = -3\frac{1}{11} \)
2. б) \( y - 4\frac{3}{5} = 2\frac{4}{5} \)
   \( y = 2\frac{4}{5} + 4\frac{3}{5} \)
   \( y = (2+4) + (\frac{4}{5} + \frac{3}{5}) = 6 + \frac{7}{5} = 6 + 1\frac{2}{5} = 7\frac{2}{5} \)
3. в) \( 8\frac{16}{27} - (x - 2\frac{17}{27}) = 5\frac{8}{27} \)
   \( x - 2\frac{17}{27} = 8\frac{16}{27} - 5\frac{8}{27} \)
   \( x - 2\frac{17}{27} = (8-5) + (\frac{16}{27} - \frac{8}{27}) = 3 + \frac{8}{27} = 3\frac{8}{27} \)
   \( x = 3\frac{8}{27} + 2\frac{17}{27} \)
   \( x = (3+2) + (\frac{8}{27} + \frac{17}{27}) = 5 + \frac{25}{27} = 5\frac{25}{27} \)

Ответ: а) \( z = -3\frac{1}{11} \); б) \( y = 7\frac{2}{5} \); в) \( x = 5\frac{25}{27} \).