4) 1 : 2 7/9 = x + 4 2/5 x;

1 : 2 7/9 = 1 : (25/9) = 9/25 = x + 4 2/5 x = x + (22/5)x = (27/5)x. Therefore, x = (9/25) * (5/27) = 1/15.