PLEASE ANSWER QUICKLY Which of the following is the correct graph of the compound inequality 4p + 1 > -15 and 6p + 3 < 45? o
7
-7 -6 -5
-3 -2 -1
0
1
2
3
4
5
6
8
9 10 11
O
-7 -6 -5 -4
O
7
-3 -2 -1
0
1
2
3
4
5
6
8
9 10 11
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9 10 11
- 7 -6 -5 -4 -3 -2 -1
0 1 2
3
4
5
6
7
8
9 10 11

  the first choice

Step-by-step explanation:

The solutions to the inequalities are ...

  4p +1 > -15

  4p > -16 . . . . . . subtract 1

  p > -4 . . . . . . . . divide by 4

This is enough to eliminate the 2nd and 4th choices.

We observe that the second inequality has a < symbol, so the graph of its solution will end with an open dot. Only the first choice has an open dot at the other end of the line segment.

You can solve the second inequality to confirm this answer.

  6p +3 < 45

  6p < 42 . . . . . . subtract 3

  p < 7 . . . . . . . . divide by 6

Then the complete solution of the two inequalities is ...

  -4 < p < 7

The appropriate graph will have open dots at -4 and 7, and will be shaded between them.