8. а) \(6-(2,2x-1\frac{1}{7})\cdot1\frac{1}{6}=5,5\); б) \(5\frac{6}{7}\left(2\frac{1}{4}-0,25x\right)=0,41\).

а)

Преобразуем числа: \(1\frac{1}{7}=\frac{8}{7}\), \(1\frac{1}{6}=\frac{7}{6}\), \(5,5=\frac{11}{2}\).

\(6-\left(2,2x-\frac{8}{7}\right)\cdot\frac{7}{6}=\frac{11}{2}\)

\(\left(2,2x-\frac{8}{7}\right)\cdot\frac{7}{6}=\frac{1}{2}\)

\(2,2x-\frac{8}{7}=\frac{1}{2}\cdot\frac{6}{7}=\frac{3}{7}\)

\(2,2x=\frac{3}{7}+\frac{8}{7}=\frac{11}{7}\)

\(\frac{11}{5}x=\frac{11}{7}\), поэтому \(x=\frac{5}{7}\).

б)

\(5\frac{6}{7}=\frac{41}{7}\), \(2\frac{1}{4}=\frac{9}{4}\), \(0,25=\frac{1}{4}\), \(0,41=\frac{41}{100}\).

\(\frac{41}{7}\left(\frac{9}{4}-\frac{x}{4}\right)=\frac{41}{100}\)

\(\frac{9}{4}-\frac{x}{4}=\frac{1}{100}\cdot7=\frac{7}{100}\)

\(\frac{225}{100}-\frac{25x}{100}=\frac{7}{100}\)

\(225-25x=7\,;\quad 25x=218\,;\quad x=\frac{218}{25}=8,72\).

Ответ: а) \(x=\frac{5}{7}\); б) \(x=8,72\).