someone explain in simple english how to solve inequalities using multiplicatino and division please

This is often confusing.....You just have to remember to "reverse" the inequality sign if you multiply or divide by a negative..

Example

3x >  6      divide both sides by 3

x  > 2   and this is true because if x = 4.....then  3(4) > 6  →  12 > 6

But, notice.....what if we had.....

-3x  > 6     divide both sides by -3 and reverse the sign

x <  -2       the reason for this is that if we kept the sign  as  ">"    we'd have an error

Note the error, here......

-3x >  6     divide by -3 and don't reverse the sign

x > -2        but if x > -2, then 0 should work in the original problem, right???

But  -3(0) > 6   =   0 > 6    and this clearly isn't true

So....by reversing the sign  we have x < -2   so..... something like -4 should work in the original problem

So.....

-3(-4) > 6    implies that 12 > 6 and that's true......!!!

So....just remember.....multiplying or dividing by a negative means that we have to reverse the signs  !!!