Including the Edge

With ≥ the fraction may also equal 0. Take (x - 1)/(x + 3) >= 0. A fraction is 0 when its top is 0, so x = 1 gives 0 over 4, which is 0, and 0 is at least 0. The top's zero belongs in the answer.

The bottom's zero is different. At x = -3 the fraction is -4 over 0, which has no value at all, so -3 is never in the answer. That is why the sign cases keep the bottom strict: the cases are x - 1 >= 0 and x + 3 > 0, or x - 1 <= 0 and x + 3 < 0.

The first case gives x >= 1, since any x of at least 1 is also above -3. The second gives x < -3. So the answer is x < -3 or x >= 1: a closed end at the top's zero, an open end at the bottom's.