Question

Solve each compound inequality 3 < 2p - 3 ≤ 13.

a) p < 8
b) p > 8
c) p < 5
d) p > 5

Answer 1

To solve the compound inequality 3 < 2p - 3 ≤ 13, we need to solve two separate inequalities and find the values of p that satisfy both of them. The solution is p > 8. The correct option is b) p > 8

Step-by-step explanation:

To solve the compound inequality 3 < 2p - 3 ≤ 13, we need to solve two separate inequalities and find the values of p that satisfy both of them.

First, we solve the left inequality: 3 < 2p - 3. We add 3 to both sides to isolate the variable:
3 + 3 < 2p - 3 + 3
6 < 2p

Then, we solve the right inequality: 2p - 3 ≤ 13. We add 3 to both sides to isolate the variable:
2p - 3 + 3 ≤ 13 + 3
2p ≤ 16

Now, we divide both sides of both inequalities by 2 to solve for p:
6/2 < p
3 < p

p ≤ 16/2
p ≤ 8

So, the solution to the compound inequality is p > 3 and p ≤ 8. This means the correct answer is p > 8.