Solve the equation, and check your solution. \[ 11 x-3(x-4)=8 x+3 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). (Simplify your answer.) B. The solution set is \{all real numbers\}. C. The solution set is \( \varnothing \).

We begin with the equation: \[ 11x - 3(x - 4) = 8x + 3 \] **Step 1: Distribute and simplify.** Distribute \(-3\) across \((x-4)\): \[ 11x - 3x + 12 = 8x + 3. \] Combine like terms on the left-hand side: \[ 8x + 12 = 8x + 3. \] **Step 2: Isolate the variable terms.** Subtract \(8x\) from both sides: \[ 8x + 12 - 8x = 8x + 3 - 8x, \] which simplifies to: \[ 12 = 3. \] **Step 3: Analyze the contradiction.** The equation \(12 = 3\) is a contradiction, meaning there is no value of \(x\) that can satisfy the equation. **Step 4: Conclusion.** Since the equation leads to a contradiction, the solution set is empty. The correct choice is: C. The solution set is \( \varnothing \).