Реши уравнение: \((x+\frac{2}{19})+5\frac{11}{38}=7\frac{41}{76}\).

\[x+\frac{2}{19}=7\frac{41}{76}-5\frac{11}{38}\]

Приведём дроби к знаменателю \(76\): \(\frac{2}{19}=\frac{8}{76}\), \(\frac{11}{38}=\frac{22}{76}\).

\[x+\frac{8}{76}=7\frac{41}{76}-5\frac{22}{76}=2\frac{19}{76}\]

\[x=2\frac{19}{76}-\frac{8}{76}=2\frac{11}{76}\]

Ответ: \(x=2\frac{11}{76}\).