12/q≤5 is another way of stating the question. So 12≤5q or 5q≥12 so q≥12/5 or q≥2.4.
Example: if q=2.5 12/2.5=24/5=4.8<5. OK. If q=3, 12/3=4<5 OK. If q=2.4 12/2.4=120/24=5, so the inequality holds, because the result is 5 and the requirement is that 12/q is at most 5.
If we put q=2 (which is not greater than 2.4) we would not expect the inequality to be true: 12/2=6>5, so it isn't true, and now we are confident that the solution is q≥2.4.