El planteamiento de las ecuaciones carece de paréntesis para dar claridad sobre las operaciones a desarrollar así que las inferiré :
x - 7 / 2 = (x / 3) + 1
x - x / 3 = 1 + 7 / 2
2x / 3 = 9 / 2
x = (9 / 2) * (3 / 2)
x = 27 / 4
(5x / 3) - 7 / 2 = (x / 3) + 1
x(5 / 3 - 1 / 3) = 1 + 7 / 2
4 / 3 x = 9 / 2
x = (9 / 2) * (3 / 4)
x = 27 / 8
(3x / 2) - 4 = (9 / 8) + x
x(3 / 2 - 2 / 2) = 4 + 9 / 8
1 / 2 x = 32 / 8 + 9 / 8
1 / 2 x = 41 / 8
x = 2 * (41 / 8)
x = 82 / 8
x = 41 / 4
4x - 5 / 3 = 6
4x = 18 / 3 + 5 / 3
4x = 23 / 3
x = (1 / 4) * (23 / 3)
x = 23 / 12
4x - 48 / 6 + x - 1 = 143 / 13
4x - 8 + x - 1 = 11
5x - 9 = 11
5x = 11 + 9
5x = 20
x = 20 / 5
x = 4
x / 4 + 3 / 2 = x / 2 + 5 / 3
x / 4 - x / 2 = 5 / 3 - 3 / 2
x / 4 - 2x / 4 = 10 / 6 - 9 / 6 - x / 4 = 1 / 6
x = - 4 * (1 / 6)
x = - 4 / 6
x = - 2 / 3
1 / 4 - 2x = (4x / 3) - 6 / 2
1 / 4 - 2x = (4x / 3) - 3 - 2x - (4x / 3) = - 3 - 1 / 4
x ( - 6 / 3 - 4 / 3) = - 12 / 4 - 1 / 4 - 10 / 3 x = - 13 / 4
x = ( - 13 / 4) * (3 / - 10)
x = 39 / 40
(8 / 3) x - 1 / 2 = (x / 8) - 6
x(8 / 3 - 1 / 8) = 1 / 2 - 6
x(64 / 24 - 3 / 24) = 1 / 2 - 12 / 2
61 / 24 x = - 11 / 2
x = ( - 11 / 2) * ( 24 / 61)
x = - 264 / 122
x = - 132 / 61
3x / 2 - 4 = 9 / 8 + x
x(3 / 2 - 2 / 2) = 9 / 8 + 32 / 8
1 / 2 x = 41 / 8
x = 2 * 41 / 8
x = 82 / 8
x = 41 / 4
3x - 1 / 4 = 6 / 5
3x = 6 / 5 + 1 / 4
3x = 24 / 20 + 5 / 20
3x = 29 / 20
x = 3 * (29 / 20)
x = 87 / 20
Saludos.