A student solves the inequality $-4x>12$ and concludes that $x>-3$. Which statement correctly identifies the student's error and provides the proper solution?

The student failed to reverse the inequality sign when dividing by a negative number; the correct solution is .

The student made an arithmetic error when dividing $12$ by $-4$; the correct solution is $x>3$.

The student should have added $4$ to both sides instead of dividing; the correct solution is $x>16$.

The student correctly solved the inequality, as the sign only flips when multiplying, not when dividing.