и) \frac{2}{5}z + 3\frac{2}{3} - \frac{7}{15} z = 2\frac{1}{2};

и) \(\frac{2}{5}z + 3\frac{2}{3} - \frac{7}{15} z = 2\frac{1}{2}\)

1. \(\frac{2}{5}z - \frac{7}{15} z = \frac{2}{5}z \cdot \frac{3}{3} - \frac{7}{15} z = \frac{6}{15}z - \frac{7}{15} z = -\frac{1}{15}z\)
2. \(3\frac{2}{3} = \frac{11}{3}\)
3. \(2\frac{1}{2} = \frac{5}{2}\)
4. \(-\frac{1}{15}z + \frac{11}{3} = \frac{5}{2}\)
5. \(-\frac{1}{15}z = \frac{5}{2} - \frac{11}{3}\)
6. \(-\frac{1}{15}z = \frac{5 \cdot 3}{2 \cdot 3} - \frac{11 \cdot 2}{3 \cdot 2}\)
7. \(-\frac{1}{15}z = \frac{15}{6} - \frac{22}{6}\)
8. \(-\frac{1}{15}z = -\frac{7}{6}\)
9. \(z = -\frac{7}{6} : (-\frac{1}{15})\)
10. \(z = \frac{7}{6} \cdot \frac{15}{1}\)
11. \(z = \frac{7 \cdot 5}{2 \cdot 1}\)
12. \(z = \frac{35}{2}\)
13. \(z = 17\frac{1}{2}\)

Ответ: 17,5