№3. Решите уравнения: 1)x+1=10 2)x-25-20 3) 37-x=74.

Ответ: 1) x=11/18; 2) x=61/100; 3) x=19/74

1) \(x + \frac{1}{6} = \frac{13}{18}\)

\(x = \frac{13}{18} - \frac{1}{6}\)

\(x = \frac{13}{18} - \frac{1 \cdot 3}{6 \cdot 3}\)

\(x = \frac{13}{18} - \frac{3}{18}\)

\(x = \frac{13 - 3}{18}\)

\(x = \frac{10}{18}\)

\(x = \frac{5}{9}\)

2) \(x - \frac{16}{25} = \frac{17}{20}\)

\(x = \frac{17}{20} + \frac{16}{25}\)

\(x = \frac{17 \cdot 5}{20 \cdot 5} + \frac{16 \cdot 4}{25 \cdot 4}\)

\(x = \frac{85}{100} + \frac{64}{100}\)

\(x = \frac{85 + 64}{100}\)

\(x = \frac{149}{100}\)

3) \(\frac{25}{37} - x = \frac{9}{74}\)

\(x = \frac{25}{37} - \frac{9}{74}\)

\(x = \frac{25 \cdot 2}{37 \cdot 2} - \frac{9}{74}\)

\(x = \frac{50}{74} - \frac{9}{74}\)

\(x = \frac{50 - 9}{74}\)

\(x = \frac{41}{74}\)

Ответ: 1) x=11/18; 2) x=61/100; 3) x=19/74