\((7\frac{3}{8}-x\cdot\frac{2}{7})-x\cdot\frac{17}{28}=2-\frac{26}{27}\)

Упростим правую часть и раскроем скобки:

\[7\frac{3}{8}-x\cdot\frac{2}{7}-x\cdot\frac{17}{28}=2-\frac{26}{27}\]

\[\frac{59}{8}-x\left(\frac{2}{7}+\frac{17}{28}\right)=\frac{28}{27}\]

\[\frac{2}{7}+\frac{17}{28}=\frac{8}{28}+\frac{17}{28}=\frac{25}{28}\]

\[\frac{59}{8}-\frac{25}{28}x=\frac{28}{27}\]

Перенесём свободные члены:

\[\frac{25}{28}x=\frac{59}{8}-\frac{28}{27}=\frac{1369}{216}\]

\[x=\frac{1369}{216}\cdot\frac{28}{25}=\frac{9583}{1350}\]

Ответ: \(x=\frac{9583}{1350}=7\frac{83}{1350}\).