№3. Решите уравнения:

Решение:

1. \( x + \frac{1}{6} = \frac{13}{18} \)
   \( x = \frac{13}{18} - \frac{1}{6} = \frac{13}{18} - \frac{1 \cdot 3}{6 \cdot 3} = \frac{13}{18} - \frac{3}{18} = \frac{13-3}{18} = \frac{10}{18} = \frac{5}{9} \)
2. \( x - \frac{25}{74} = \frac{16}{17} \)
   \( x = \frac{16}{17} + \frac{25}{74} = \frac{16 \cdot 74}{17 \cdot 74} + \frac{25 \cdot 17}{74 \cdot 17} = \frac{1184}{1258} + \frac{425}{1258} = \frac{1184+425}{1258} = \frac{1609}{1258} \)
3. \( \frac{17}{18} - \frac{2}{3} + x = \frac{1}{6} \)
   \( x = \frac{1}{6} - \frac{17}{18} + \frac{2}{3} = \frac{1 \cdot 3}{6 \cdot 3} - \frac{17}{18} + \frac{2 \cdot 6}{3 \cdot 6} = \frac{3}{18} - \frac{17}{18} + \frac{12}{18} = \frac{3-17+12}{18} = \frac{-14+12}{18} = \frac{-2}{18} = -\frac{1}{9} \)
4. \( \frac{49}{72} + \frac{8}{9} - x = \frac{23}{36} \)
   \( x = \frac{49}{72} + \frac{8}{9} - \frac{23}{36} = \frac{49}{72} + \frac{8 \cdot 8}{9 \cdot 8} - \frac{23 \cdot 2}{36 \cdot 2} = \frac{49}{72} + \frac{64}{72} - \frac{46}{72} = \frac{49+64-46}{72} = \frac{113-46}{72} = \frac{67}{72} \)

Ответ: 1) \( x = \frac{5}{9} \); 2) \( x = \frac{1609}{1258} \); 3) \( x = -\frac{1}{9} \); 4) \( x = \frac{67}{72} \).