Solve the compound inequality. Graph the solutions. -5 < 2p - 3 <= 11

Answer 1

To solve the compound inequality -5 < 2p - 3 ≤ 11, we will solve the two separate inequalities and then combine the solutions.

First, let's solve 2p - 3 ≤ 11:

Add 3 to both sides:
2p - 3 + 3 ≤ 11 + 3
2p ≤ 14

Divide both sides by 2:
2p/2 ≤ 14/2
p ≤ 7

Next, let's solve -5 < 2p - 3:

Add 3 to both sides:
-5 + 3 < 2p - 3 + 3
-2 < 2p

Divide both sides by 2:
-2/2 < 2p/2
-1 < p

Now, let's combine the solutions.

The solution to -5 < 2p - 3 ≤ 11 is p ∈ (-1, 7].
This means that p is greater than -1 and less than or equal to 7.

To graph this solution on a number line, draw a closed circle at 7 and an open circle at -1. Then, shade the region between the two circles to represent the solution.