All right so you have -8 < 2x + 4 <= -2
So you want to isolate X
In order to do that, first subtract four from all of the terms
-8 - 4 < 2x + 4 - 4 <= -2 - 4
-12 < 2x <= -6
Then divide all pieces by the coefficient of X to isolate it entirely
-12/2 < 2x/2 <= -6/2
-6 < x <= -3
Do you know how to graph that?
Your teacher just wants a number line, right?
For the next one, you've got an easier time because you don't need to add or subtract anything; just divide to isolate Z
However, if you divide inequalities by a negative number, their direction is reversed. This might not make much sense by itself, but watch.
-6 <= -2z <= 4
-6/-2 >= -2z/-2 >= 4/-2
3 >= z >= -2
I'll see if I can catch up on this in the morning, but I need to get some sleep right now. Good luck. I'm not the best at explaining things.
Just think about the direction reversed this way.
if you have x > 2, and then divide or multiply both sides by -1
you would have -x > -2
All values that previously functioned in this inequality (say x = 4 or 5, both being greater than 2) will NOT function in -x > -2
-4 > -2 is not true
-5 > -2 is not true
Equality does not have this issue because it is in a certain sense symmetrical; if A = B, then B = A, no matter how you look at it.
If you're dealing with >=, the equality will remain, and then the > is subject to change.
