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 !!!
