5.416 Найдите корень уравнения: a) \(\frac{1}{3}\) + x = \(\frac{5}{6}\); б) x - \(\frac{2}{5}\) = \(\frac{3}{10}\); в) x + \(\frac{4}{18}\) = \(\frac{5}{6}\) + \(\frac{1}{3}\); г) (\(\frac{9}{10}\) - x) + \(\frac{9}{15}\) = 1.

Решим уравнения:

1. а) \(\frac{1}{3}\) + x = \(\frac{5}{6}\) \(x = \frac{5}{6} - \frac{1}{3}\) \(x = \frac{5}{6} - \frac{2}{6}\) \(x = \frac{3}{6}\) \(x = \frac{1}{2}\)
   Ответ: \(\frac{1}{2}\)
2. б) x - \(\frac{2}{5}\) = \(\frac{3}{10}\) \(x = \frac{3}{10} + \frac{2}{5}\) \(x = \frac{3}{10} + \frac{4}{10}\) \(x = \frac{7}{10}\)
   Ответ: \(\frac{7}{10}\)
3. в) x + \(\frac{4}{18}\) = \(\frac{5}{6}\) + \(\frac{1}{3}\) \(x + \frac{2}{9} = \frac{5}{6} + \frac{1}{3}\) \(x = \frac{5}{6} + \frac{1}{3} - \frac{2}{9}\) \(x = \frac{15}{18} + \frac{6}{18} - \frac{4}{18}\) \(x = \frac{17}{18}\)
   Ответ: \(\frac{17}{18}\)
4. г) (\(\frac{9}{10}\) - x) + \(\frac{9}{15}\) = 1 \(\frac{9}{10}\) - x + \(\frac{3}{5}\) = 1 \(\frac{9}{10}\) + \(\frac{6}{10}\) - x = 1 \(\frac{15}{10}\) - x = 1 1\(\frac{5}{10}\) - x = 1 1\(\frac{1}{2}\) - x = 1 \(x = 1\frac{1}{2} - 1\) \(x = \frac{1}{2}\)
   Ответ: \(\frac{1}{2}\)