Question

Help please!

Answer 1

4p+1>-11 or 6p+3<39 is the compound inequality. Let's simplify these separately.

4p+1>-11
4p+1-1>-11-1
4p>-12
4p/4>-12/4
***p>-3***

6p+3<39
6p+3-3<39-3
6p<36
6p/6<36/6
***p<6***

There must be an open circle on -3 and an open circle on 6. But which directions should the graph point?

p<6 indicates that, from the open circle on 6, everything to the left extending forever should be shaded.
However, p>-3 indicates that, from the open circle on -3, everything to the right extending forever should be shaded.

The two graphs overlap, and we say that the solution is "all reals." This is graphed as choice D.