3<2p-5≤11

Answer 1

To find the range of values for p that satisfy the inequality 3 < 2p - 5 ≤ 11, we can solve it in two steps.

Step 1: Solve the first inequality:
3 < 2p - 5

Add 5 to both sides:
3 + 5 < 2p - 5 + 5
8 < 2p

Divide both sides by 2:
8/2 < 2p/2
4 < p

So the first inequality is p > 4.

Step 2: Solve the second inequality:
2p - 5 ≤ 11

Add 5 to both sides:
2p - 5 + 5 ≤ 11 + 5
2p ≤ 16

Divide both sides by 2:
2p/2 ≤ 16/2
p ≤ 8

So the second inequality is p ≤ 8.

Combining the two inequalities, we have:
4 < p ≤ 8

Thus, the range of values for p that satisfy the inequality is 4 < p ≤ 8.