Let's simplify the equation step by step.

1/2 (x-1) + 1/14 = -2/7 (3-x)

1/2 x - 1/2 + 1/14 = -6/7 + 2/7 x

1/2 x - 1/2 + 1/14 = -6/7 + 2/7 x

Multiplying by 14 to get rid of the fractions:

7 x - 7 + 1 = -12 + 4 x

7 x - 6 = -12 + 4 x

Rearranging the terms:

7x - 4x = -6 - 12

3x = -18

Dividing by 3:

x = -6

Therefore, the solution to the equation is x = -6.