Решение:
$$ (x + 4\frac{9}{11}) - 5\frac{6}{11} = 1\frac{8}{11} $$
$$ x + 4\frac{9}{11} = 1\frac{8}{11} + 5\frac{6}{11} $$
$$ x + 4\frac{9}{11} = 6\frac{14}{11} $$
$$ x + 4\frac{9}{11} = 7\frac{3}{11} $$
$$ x = 7\frac{3}{11} - 4\frac{9}{11} $$
$$ x = 6\frac{14}{11} - 4\frac{9}{11} $$
$$ x = 2\frac{5}{11} $$
Ответ: $$x = 2\frac{5}{11} $$.