I was given summer calc homework to help prepare for the year. The first problem is extremely confusing! I have never, ever come across a problem like this before in any of my math classes, and we were not given books to help us, so I'm stuck. Please help me? Thanks in advance!
1). If 2 < x < 6, which of the following statements about x are necessarily true and which are not necessarily true? Use NT for necessarily true and NNT for not necessarily true.
a). 0 < x < 4
b). 0 < x-2 < 4
c). 1< x/2 < 3
d). 1/6 < 1/x < 1/2
e). 1< 6/x < 3
f). |x-4| < 2
g). -6 < -x <2
h). -6 < -x < -2
That is the whole problem. I tried to figure out a. I thought maybe since 2 < x < 6, that x= 3, 4, or 5. Since a reads 0 < x < 4... that x would have to be 3...but the original its 3 4 and 5. So I put that its NNT. Now I'm pretty sure that I did that all wrong to begin with....but its all have have to start out with.
I understand that I have to draw a number line and find the domain...but I forget how to do both for (a-h). I don't believe I've ever had to do this!