Question

Why must you flip the inequality symbol when you divide by a negative number?

Answer 1

Actually, I can show you why you have to do it even though you don't really have to do it. There's another way to solve them

Answer 2

Suppose you had -3x < 9

Well, the first impulse is to divide both sides by -3 and flip the sign, right? Well you don't have to do that. Alternatively you can add 3x to both sides, then subtract 9 from both sides to get this:

-9 < 3x

Now you can divide both sides by 3 to get:

-3 < x

I solved for x without flipping the sign. Which eliminates confusion.

Answer 3

@Babrina11 let us take and example
-11<12
now if you multiply by negative on both sides the inequality becomes
11<-12 as we know (-ve)(-ve)=+ve
but this cannot be true since a positive number is always greater than a negative number
so 11>-12 that is why we flip signs