5. Решите уравнение: 1) \(7\frac{5}{8}x = 2\frac{5}{16}\); 2) \((x + \frac{5}{12}) - \frac{9}{20} = \frac{11}{15}\)

1) \(7\frac{5}{8}x = 2\frac{5}{16}\)

\(\frac{61}{8}x = \frac{37}{16}\)

\(x = \frac{37}{16} : \frac{61}{8}\)

\(x = \frac{37}{16} \cdot \frac{8}{61}\)

\(x = \frac{37}{2 \cdot 61} = \frac{37}{122}\)

2) \((x + \frac{5}{12}) - \frac{9}{20} = \frac{11}{15}\)

\(x + \frac{5}{12} = \frac{11}{15} + \frac{9}{20}\)

\(x + \frac{5}{12} = \frac{11 \cdot 4 + 9 \cdot 3}{60}\)

\(x + \frac{5}{12} = \frac{44 + 27}{60}\)

\(x + \frac{5}{12} = \frac{71}{60}\)

\(x = \frac{71}{60} - \frac{5}{12}\)

\(x = \frac{71 - 5 \cdot 5}{60}\)

\(x = \frac{71 - 25}{60}\)

\(x = \frac{46}{60}\)

\(x = \frac{23}{30}\)

Ответ: 1) \(\frac{37}{122}\); 2) \(\frac{23}{30}\)