Question

How many integers $n$ satisfy $-4n\ge 12$ and $n+5>2$??

Answer 1

-4n ≥ 12   ==>   n ≤ -3

n + 5 > 2   ==>   n > -3

But n cannot be both less than/equal to -3 AND greater than -3, so there are no integers n that satisfy these inequalities.