Can we throw around terms in an inequality equation?

I was going through GregMat medium quant practice session and stumbled upon this question. For this, the obvious elimination of values for x are -2 & -4, but also -1 & -3 if you divide both sides by (x+1)(x+3). I know this operation will change the inequality sign but I don’t think it will change what values are invalid. For the above reason, I think the answer should be the 2nd option since it captures a set of values valid for the inequality. I don’t know the official answer as Greg didn’t say what was the final answer but he eliminated the 2nd option.

The question is at GregMat - GregMat for you to try.