To solve for x, we can first combine the fractions on the left side of the equation:

1/2 + 1/2 * x = 5/6
1/2 + x/2 = 5/6

Next, we can multiply both sides of the equation by 2 to get rid of the fraction:

2 * (1/2 + x/2) = 2 * 5/6
1 + x = 10/6
1 + x = 5/3

Now, we can isolate x by subtracting 1 from both sides:

x = 5/3 - 1
x = 5/3 - 3/3
x = 2/3

Therefore, the solution to the equation is x = 2/3.