Step 1 :Find a common denominator for the fractions: \(\text{lcm}(4, 3) = 12\)
Step 2 :Multiply each term by the common denominator: \(12\left(\frac{3x}{4} - \frac{2x}{3}\right) = 12\left(\frac{1}{2}\right)\)
Step 3 :Simplify the equation: \(9x - 8x = 6\)
Step 4 :Solve for x: \(x = 6\)
Step 5 :\(\boxed{x = 6}\)