Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. \( \frac{x}{3}-\frac{11}{12} \leq \frac{x}{4}+1 \) 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 \( \varnothing \). (Type your answer using interval notatidn.)

To solve the inequality \( \frac{x}{3}-\frac{11}{12} \leq \frac{x}{4}+1 \), first, we'll combine like terms. Start by eliminating the fractions by multiplying through by 12, the least common multiple of the denominators: \[ 12 \left( \frac{x}{3} \right) - 12 \left( \frac{11}{12} \right) \leq 12 \left( \frac{x}{4} \right) + 12(1) \] This simplifies to: \[ 4x - 11 \leq 3x + 12 \] Next, isolate \(x\) by subtracting \(3x\) from both sides: \[ x - 11 \leq 12 \] Then add 11 to both sides: \[ x \leq 23 \] This gives us the solution set in interval notation as \((- \infty, 23]\). To graph this on a number line, draw a line that extends infinitely to the left with a closed circle at 23, indicating that 23 is included in the solution set. So the final answer is: A. The solution set is \((- \infty, 23]\).