Find the solution set. Then indicate whether the equation is conditional, an identity, or a contradiction. \( 3(y+8)-8(3 y-4)=-21 y+4 \) Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is \( \} \). B. The solution is the set of all real numbers. C. The solution is the empty set.

To solve the equation \( 3(y+8)-8(3y-4)=-21y+4 \), we first expand both sides: 1. Distributing on the left side: \[ 3y + 24 - 24y + 32 = -21y + 4 \] This simplifies to: \[ -21y + 56 = -21y + 4 \] 2. Now, we isolate the variables: \[ 56 \neq 4 \] This means we have a false statement. Since we have reached an inconsistency, the equation does not hold true for any value of \( y \). Therefore, the solution set is the empty set, indicating that this equation is a contradiction. So the correct choice is: C. The solution is the empty set.