solve the compound inequality. Graph the solutions.
1<2p-7≤9
To solve the compound inequality 1 < 2p - 7 ≤ 9, we need to solve each inequality separately and then find the intersection of their solutions.
First, let's solve the inequality 1 < 2p - 7:
1 < 2p - 7
Add 7 to both sides:
8 < 2p
Divide both sides by 2:
4 < p
Now, let's solve the second inequality 2p - 7 ≤ 9:
2p - 7 ≤ 9
Add 7 to both sides:
2p ≤ 16
Divide both sides by 2:
p ≤ 8
So we have found that p needs to satisfy the inequalities 4 < p and p ≤ 8.
To graph the solution, we will use a number line. We will mark an open circle at 4 to represent the inequality 4 < p, and a closed circle at 8 to represent the inequality p ≤ 8. Then we will shade the area between these two points since p needs to satisfy both inequalities.
<----|-----|-----|-----|-----[O)=====(O]-----|-----|----->
0 4 8 12 16 20 24 28 32
The shaded region between the open circle (4) and the closed circle (8) represents the solution to the compound inequality 1 < 2p - 7 ≤ 9.