№6. Решите уравнения: а) \(x - 4 \frac{3}{23} = 2 \frac{22}{23}\); б) \(10 \frac{10}{17} - (x + \frac{2}{17}) = 8 \frac{9}{17}\); в) \((x - 2 \frac{1}{8}) : 7 \frac{5}{6} = 1\).

а) \(x - 4 \frac{3}{23} = 2 \frac{22}{23}\)

1. \(x = 2 \frac{22}{23} + 4 \frac{3}{23}\)
2. \(x = (2 + 4) + (\frac{22}{23} + \frac{3}{23})\)
3. \(x = 6 + \frac{25}{23}\)
4. \(x = 6 + 1 \frac{2}{23}\)
5. \(x = 7 \frac{2}{23}\)

Ответ: \(7 \frac{2}{23}\)

б) \(10 \frac{10}{17} - (x + \frac{2}{17}) = 8 \frac{9}{17}\)

1. \(x + \frac{2}{17} = 10 \frac{10}{17} - 8 \frac{9}{17}\)
2. \(x + \frac{2}{17} = (10 - 8) + (\frac{10}{17} - \frac{9}{17})\)
3. \(x + \frac{2}{17} = 2 + \frac{1}{17}\)
4. \(x = 2 \frac{1}{17} - \frac{2}{17}\)
5. \(x = 1 \frac{18}{17} - \frac{2}{17}\)
6. \(x = 1 \frac{16}{17}\)

Ответ: \(1 \frac{16}{17}\)

в) \((x - 2 \frac{1}{8}) : 7 \frac{5}{6} = 1\)

1. \(x - 2 \frac{1}{8} = 1 \cdot 7 \frac{5}{6}\)
2. \(x - 2 \frac{1}{8} = 7 \frac{5}{6}\)
3. \(x = 7 \frac{5}{6} + 2 \frac{1}{8}\)
4. \(x = 7 \frac{20}{24} + 2 \frac{3}{24}\)
5. \(x = 9 \frac{23}{24}\)

Ответ: \(9 \frac{23}{24}\)