к) 3\frac{1}{2} \cdot (\frac{2}{3}x + \frac{4}{7}) = 2\frac{1}{3};

к) \(3\frac{1}{2} \cdot (\frac{2}{3}x + \frac{4}{7}) = 2\frac{1}{3}\)

1. \(\frac{7}{2} \cdot (\frac{2}{3}x + \frac{4}{7}) = \frac{7}{3}\)
2. \(\frac{2}{3}x + \frac{4}{7} = \frac{7}{3} : \frac{7}{2}\)
3. \(\frac{2}{3}x + \frac{4}{7} = \frac{7}{3} \cdot \frac{2}{7}\)
4. \(\frac{2}{3}x + \frac{4}{7} = \frac{2}{3}\)
5. \(\frac{2}{3}x = \frac{2}{3} - \frac{4}{7}\)
6. \(\frac{2}{3}x = \frac{2 \cdot 7}{3 \cdot 7} - \frac{4 \cdot 3}{7 \cdot 3}\)
7. \(\frac{2}{3}x = \frac{14}{21} - \frac{12}{21}\)
8. \(\frac{2}{3}x = \frac{2}{21}\)
9. \(x = \frac{2}{21} : \frac{2}{3}\)
10. \(x = \frac{2}{21} \cdot \frac{3}{2}\)
11. \(x = \frac{2 \cdot 3}{21 \cdot 2}\)
12. \(x = \frac{1}{7}\)

Ответ: 1/7