Решите уравнение 4) 1/3 х+1/4 х+1/5 х=1 19/75

1/3 * х + 1/4 * х + 1/5 * х = 1 19/75;

(1/3 + 1/4 + 1/5) * х = 1 19/75;

((1 * 20) / (3 * 20) + (1 * 15) / (4 * 15) + (1 * 12) / (5 * 12)) * х = 1 19/75;

(20/60 + 15/60 + 12/60) * х = 1 19/75;

47/60 * х = 94/75;

х = 94/75 : 47/60;

х = 94/75 * 60/47;

х = (94 * 60) / (75 * 47);

х = 5640/3525;

х = 24/15;

х = 8/5;

х = 1 3/5.

Проверка:

1/3 * 1 3/5 + 1/4 * 1 3/5 + 1/5 * 1 3/5 = 1 19/75;

(1/3 + 1/4 + 1/5) * 8/5 = 1 19/75;

((1 * 20) / (3 * 20) + (1 * 15) / (4 * 15) + (1 * 12) / (5 * 12)) * 8/5 = 1 19/75;

(20/60 + 15/60 + 12/60) * 8/5 = 1 19/75;

47/60 * 8/5 = 94/75;

(47 * 8) / (60 * 5) = 94/75;

376/300 = 94/75;

94/75 = 94/75. Решение выполнено верно.