I'm not sure which way my sign should face at the end of the equation

Question

So far I have:

 

-6<3(x+1)≤9

-6<3x + 3≤9

-6<3x ≤6

-9<3X≤6

 

HERE is where I am questioning myself:

 

My next step would be to divide -9 by pos 3 and 6 by pos 3.

BECAUSE the nine is negative, would that change the direction of my sign in my answer?

Answer 1

I would separate the inequality: 3x > -9 

 

You seem to understand that if you divide by a negative number, you should switch the direction of the sign. However, in this case, you're dividing by a positive number (3). The -9 doesn't move. So, it should be

3x/3 > -9/3 = x > -3