To solve the equation \( 3x + 2(4x - 6) = 8x + 1 \), we will first simplify the left side of the equation.
Starting with the left side:
\[ 3x + 2(4x - 6) \]
Distributing the \(2\):
\[ 3x + 8x - 12 \]
Now, combine like terms:
\[ (3x + 8x) - 12 = 11x - 12 \]
So, the equation now becomes:
\[ 11x - 12 = 8x + 1 \]
Next, we'll move \(8x\) to the left side:
\[ 11x - 8x - 12 = 1 \]
This simplifies to:
\[ 3x - 12 = 1 \]
Now, add \(12\) to both sides:
\[ 3x = 13 \]
Finally, divide both sides by \(3\):
\[ x = \frac{13}{3} \]
Thus, the solution is:
\[ x = \frac{13}{3} \]