2/3:5/6x-1/6+1/3=7/9 решить уравнение

Решите задачу:

$\frac{2}{3} \div \frac{5}{6}x - \frac{1}{6} + \frac{1}{3} = \frac{7}{9} \\ \frac{2}{3} \div \frac{5}{6}x= \frac{7}{9} + \frac{1}{6} - \frac{1}{3} \\ \frac{2}{3} \div \frac{5}{6}x = \frac{14}{18} + \frac{3}{18} - \frac{6}{18} \\ \frac{2}{3} \div \frac{5}{6}x = \frac{11}{18} \\ \frac{5}{6}x = \frac{11}{18} \div \frac{2}{3} \\ \frac{5}{6}x = \frac{11 \times 3}{18 \times 2} \\ \frac{5}{6}x = \frac{11}{12} \\ x = \frac{11}{12} \div \frac{5}{6} \\ x = \frac{11 \times 6}{12 \times 5} \\ x = \frac{11}{10} = 1 \frac{1}{10}$