To verify if $x=-\frac{1}{2}$ is a valid solution to the linear equation $4x-2=2x+1$, apply the three-step determination strategy:

Step 1. Substitute the value for the variable: $4\left(-\frac{1}{2}\right) - 2 = 2\left(-\frac{1}{2}\right) + 1$ Step 2. Simplify expressions on both sides. Multiply first: $-2 - 2 = -1 + 1$. Then subtract and add: $-4 = 0$ Step 3. Determine if the result is true: Since $-4 = 0$ is a false mathematical statement, the value $x=-\frac{1}{2}$ is not a solution to the equation.