Solve the Linear Equation Involving a Fraction: -7x + 3 - 1/2 = 0

To solve the equation $-7x + 3 - \frac{1}{2} = 0$, follow these steps:

Step 1: Simplify the equation.
First, combine the constant terms $3$ and $-\frac{1}{2}$. Convert $3$ to a fraction as $\frac{6}{2}$ to facilitate subtraction. Thus, $3 - \frac{1}{2} = \frac{6}{2} - \frac{1}{2} = \frac{5}{2}$.
The equation now becomes: $-7x + \frac{5}{2} = 0$.

Step 2: Move the constant term to the other side.
Subtract $\frac{5}{2}$ from both sides:
$-7x + \frac{5}{2} - \frac{5}{2} = 0 - \frac{5}{2}$.
This simplifies to: $-7x = -\frac{5}{2}$.

Step 3: Isolate $x$.
Divide both sides by $-7$ to solve for $x$:
$x = \frac{-\frac{5}{2}}{-7}$.
Simplify the expression:
$x = \frac{5}{14}$.

Thus, the solution to the equation is $\boxed{\frac{5}{14}}$, which corresponds to choice 3.