Inequalities II PrepSwift Video Quiz Doubt

Hi, this is a question in the quiz after the Inequalities II PrepSwift video. I am unable to understand the solution shared for this question. Can someone please help out by explaining how to solve this?

Well, do you know how to “solve” \frac 1x > 6 ?

It will be 1/6 > x

No, you can’t multiply both sides of the inequality by x because you don’t know the sign of x. You could consider doing two cases: x > 0 and x < 0 and solve the inequality accordingly.