To solve these equations, we will perform the necessary operations to isolate the variable.

11 2/3x - 5 1/6 = 3 3/4 + 2 3/4x
11 2/3x - 5 1/6 - 2 3/4x = 3 3/4
11 2/3x - 5 1/6 - 2 3/4x = 3 3/4
11 2/3x - 2 3/4x = 3 3/4 + 5 1/6
(35/3)x - (11/4)x = (15/4) + (31/6)
(105/12)x - (33/12)x = (90/24) + (124/24)
(72/12)x = (214/24)
x = 214/24 / 72/12
x = 214/24 * 12/72
x = 214/6
x = 35 2/6
x = 35 1/3

12 3/4 + 3/7y = y/2 - 10 1/28
12 3/4 + 10 1/28 = y/2 - 3/7y
12 3/4 + 10 1/28 = (1/2 - 3/7)y
(51/4) + (285/28) = (7/14 - 6/14)y
(51/4) + (285/28) = (1/14)y
(51/4) + (285/28) = (1/14)y
(357/28) + (285/28) = (1/14)y
(642/28) = (1/14)y
(642/28) * (14/1) = y
y = 321/7
y = 45 6/7

6x + 7/7 = 3 - 5x - 3/8
6x + 1 = 3 - 5x - 3/8
6x + 5x = 3 - 1 - 3/8
11x = 2 - 3/8
11x = 13/8
x = (13/8) / 11
x = 13/88

10 - 3x - 1/2 = 6x + 3/11
10 - 1/2 = 6x + 3/11 + 3x
9 1/2 = 6x + 3/11 + 3x
9 1/2 = 9x + 3/11
9 1/2 - 3/11 = 9x
(95/2 - 3/11) / 9 = x
x = (1045/22) / 9
x = (1045/22) * (1/9)
x = 1045/198