To solve the equation 2xy - 2y + x - 7 = 0, we can rearrange the terms to group the variables together:

2xy + x - 2y - 7 = 0

Now, let's factor out the common terms:

x(2y + 1) - 2(2y + 1) = 0

Now, we can see that we have a common factor of (2y + 1):

(2y + 1)(x - 2) = 0

To find the solutions, we set each factor equal to zero:

2y + 1 = 0 or x - 2 = 0

For 2y + 1 = 0, we can solve for y:

2y = -1
y = -1/2

For x - 2 = 0, we can solve for x:

x = 2

Therefore, the solutions to the equation 2xy - 2y + x - 7 = 0 are x = 2 and y = -1/2.