Solve the equation. Check your proposed solution. \[ 4 x+\frac{1}{8}-3 x=\frac{1}{2} \] \[ x= \] (Simplify your answer. Type an integer or a simplified fraction.)

Step 1 ：Combine like terms on the left side of the equation: \(4x - 3x + \frac{1}{8} = \frac{1}{2}\) simplifies to \(x + \frac{1}{8} = \frac{1}{2}\).

Step 2 ：Subtract \(\frac{1}{8}\) from both sides of the equation: \(x + \frac{1}{8} - \frac{1}{8} = \frac{1}{2} - \frac{1}{8}\) simplifies to \(x = \frac{3}{8}\).

Step 3 ：Final Answer: The solution to the equation is \(x = \boxed{\frac{3}{8}}\).