1. x + 4\(\frac{2}{5}\)x = 1\(\frac{2}{9}\);

1. \(x + 4\frac{2}{5}x = 1\frac{2}{9}\) \(x + \frac{4 \cdot 5 + 2}{5}x = \frac{1 \cdot 9 + 2}{9}\) \(x + \frac{22}{5}x = \frac{11}{9}\) \(x(1 + \frac{22}{5}) = \frac{11}{9}\) \(x(\frac{5}{5} + \frac{22}{5}) = \frac{11}{9}\) \(x(\frac{27}{5}) = \frac{11}{9}\) \(x = \frac{11}{9} : \frac{27}{5}\) \(x = \frac{11}{9} \cdot \frac{5}{27}\) \(x = \frac{11 \cdot 5}{9 \cdot 27}\) \(x = \frac{55}{243}\)

Ответ: \(\frac{55}{243}\)