Ответ:

  1. \(x+\frac{4}{9}=\frac{11}{18}\).

    \(x=\frac{11}{18}-\frac{4}{9}=\frac{11}{18}-\frac{8}{18}=\frac{3}{18}=\frac{1}{6}\).

    Проверка: \(\frac{1}{6}+\frac{4}{9}=\frac{3}{18}+\frac{8}{18}=\frac{11}{18}\).

  2. \(x+\frac{1}{6}=\frac{4}{5}\).

    \(x=\frac{4}{5}-\frac{1}{6}=\frac{24}{30}-\frac{5}{30}=\frac{19}{30}\).

    Проверка: \(\frac{19}{30}+\frac{1}{6}=\frac{19}{30}+\frac{5}{30}=\frac{24}{30}=\frac{4}{5}\).

Ответ: а) \(x=\frac{1}{6}\); б) \(x=\frac{19}{30}\).