Solve and check the linear equation. \[ 3(x-3)+12=2(x+4) \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). B. The solution set is \( \{x \mid x \) is a real number \( \} \). C. The solution set is \( \varnothing \).

To solve the equation \( 3(x-3)+12=2(x+4) \), we first distribute and simplify both sides: 1. Distribute on the left: \( 3x - 9 + 12 = 2(x + 4) \) becomes \( 3x + 3 = 2x + 8 \). 2. Next, isolate x: Subtract \( 2x \) from both sides, resulting in \( x + 3 = 8 \). 3. Then, subtract 3 from both sides: \( x = 5 \). Now let's check our solution by substituting \( x = 5 \) back into the original equation: Left side: \( 3(5-3)+12 = 3(2)+12 = 6 + 12 = 18 \). Right side: \( 2(5+4) = 2(9) = 18 \). Both sides are equal, confirming that \( x = 5 \) is the correct solution. So, the solution set is: A. The solution set is \( \{5\} \).