Solve the Fraction Equation: Find X in 1/2(x+3) - 8x = 3

Let's solve the given equation $\frac{1}{2}(x+3) - 8x = 3$.

First, distribute the $\frac{1}{2}$ inside the parentheses:
$\frac{1}{2}(x+3) = \frac{1}{2}x + \frac{1}{2} \times 3 = \frac{1}{2}x + \frac{3}{2}$.

Substitute back into the original equation:
$\frac{1}{2}x + \frac{3}{2} - 8x = 3$.

To eliminate the fraction, multiply every term by 2 to simplify:
$2 \times \left(\frac{1}{2}x + \frac{3}{2}\right) - 2 \times 8x = 2 \times 3$.

After clearing the fraction, the equation becomes:
$x + 3 - 16x = 6$.

Combine like terms involving $x$:
$x - 16x + 3 = 6$ simplifies to $-15x + 3 = 6$.

Isolate $x$ by subtracting 3 from both sides:
$-15x = 6 - 3$.
This simplifies to $-15x = 3$.

Finally, divide both sides by $-15$ to solve for $x$:
$x = \frac{3}{-15}$,
which simplifies to $x = -\frac{1}{5}$.

Therefore, the solution to the equation $\frac{1}{2}(x+3) - 8x = 3$ is $x = -\frac{1}{5}$.