Step 1 :Find a common denominator for the fractions: \(\frac{2x-1}{6} + \frac{x-1}{4} = \frac{4(2x-1) + 6(x-1)}{12}\)
Step 2 :Combine the fractions and solve for x: \(\frac{14x-10}{12} = \frac{17}{4}\) \(\Rightarrow\) \(x = \boxed{8}\)