9 1/5-(5х-4 1/2):11 1/4=8 14/15

9 1/5 - (5 * х - 4 1/2) : 11 1/4 = 8 14/15;
(5 * х - 4 1/2) : 11 1/4 = 9 1/5 - 8 14/15;
(5 * х - 4 1/2) : 11 1/4 = 46/5 - 134/15;
(5 * х - 4 1/2) : 11 1/4 = 138/15 - 134/15;
(5 * х - 4 1/2) : 11 1/4 = 4/15;
(5 * х - 4 1/2) = 4/15 * 11 1/4;
(5 * х - 4 1/2) = 4/15 * 45/4;
(5 * х - 4 1/2) = (4 * 45)/(15 * 4);
(5 * х - 4 1/2) = 3;
5 * х = 3 + 4 1/2;
5 * х = 7 1/2;
х = 7 1/2 : 5;
х = 15/2 * 1/5;
х = 15/10;
х = 3/2;
х = 1 1/2.
Проверка:
9 1/5 - (5 * 1 1/2 - 4 1/2) : 11 1/4 = 8 14/15;
46/5 - (5 * 3/2 - 9/2) : 45/4 = 8 14/15;
46/5 - (15/2 - 9/2) : 45/4 = 8 14/15;
46/5 - 6/2 : 45/4 = 8 14/15;
46/5 - 3 * 4/45 = 8 14/15;
46/5 - 12/45 = 8 14/15;
46/5 - 4/15 = 8 14/15;
(46 * 3)/(5 * 3) - 4/15 = 8 14/15;
138/15 - 4/15 = 8 14/15;
134/15 = 8 14/15;
8 14/15 = 8 14/15. Решение верно.