Let's rewrite the equation step by step.
Starting from the original equation:
\[ \frac{1}{2}(6x + 2) = 3x \]
First, let's distribute the \(\frac{1}{2}\):
\[ \frac{1}{2} \cdot 6x + \frac{1}{2} \cdot 2 = 3x \]
This simplifies to:
\[ 3x + 1 = 3x \]
Next, we will subtract \(3x\) from both sides of the equation:
\[ 3x + 1 - 3x = 3x - 3x \]
This simplifies to:
\[ 1 = 0 \]
However, this is a contradiction (1 does not equal 0), which suggests that there is no solution to the equation.
So the final response is:
\[ 1 \neq 0 \]
Thus, the equation has no solution.