To determine if \( p = 12 \) is a solution to the equation \( 2p = 82 \), we can substitute \( p \) with 12 in the equation:
\[ 2(12) = 82 \]
Calculating the left side, we have:
\[ 24 = 82 \]
Since 24 does not equal 82, \( p = 12 \) is NOT a solution to the equation \( 2p = 82 \).
To find the correct value of \( p \), we can solve the equation \( 2p = 82 \):
\[ p = \frac{82}{2} = 41 \]
Thus, the solution to the equation is \( p = 41 \).