3. Решите уравнение: 1) 4/5 + x = 10/23 2) 7/9 - (x - 2/16) = 4/11

Решение:

1. \( \frac{4}{5} + x = \frac{10}{23} \)
   \( x = \frac{10}{23} - \frac{4}{5} \)
   \( x = \frac{10 \cdot 5 - 4 \cdot 23}{23 \cdot 5} \)
   \( x = \frac{50 - 92}{115} \)
   \( x = -\frac{42}{115} \)
2. \( \frac{7}{9} - \left( x - \frac{2}{16} \right) = \frac{4}{11} \)
   \( \frac{7}{9} - \left( x - \frac{1}{8} \right) = \frac{4}{11} \)
   \( x - \frac{1}{8} = \frac{7}{9} - \frac{4}{11} \)
   \( x - \frac{1}{8} = \frac{7 \cdot 11 - 4 \cdot 9}{9 \cdot 11} \)
   \( x - \frac{1}{8} = \frac{77 - 36}{99} \)
   \( x - \frac{1}{8} = \frac{41}{99} \)
   \( x = \frac{41}{99} + \frac{1}{8} \)
   \( x = \frac{41 \cdot 8 + 1 \cdot 99}{99 \cdot 8} \)
   \( x = \frac{328 + 99}{792} \)
   \( x = \frac{427}{792} \)

Ответ: 1) \(x = -\frac{42}{115}\); 2) \(x = \frac{427}{792}\).