To solve for x, we can start by simplifying the equation:
x - 1 = (1/2)x + 5/2
Next, let's get rid of the fractions by multiplying every term in the equation by the least common multiple (LCM) of the denominators, which is 2:
2(x - 1) = 2((1/2)x + 5/2)
Simplifying further:
2x - 2 = x + 5
Next, let's isolate x by moving all terms with x to one side of the equation:
2x - x = 5 + 2
Simplifying further:
x = 7
Answer: \boxed{x = 7}