3<2p-5≤11
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.
To solve the inequality 3 < 2p - 5 ≤ 11, we will solve it in steps.
Step 1: Solve the first inequality: 3 < 2p - 5
Add 5 to both sides of the inequality:
3 + 5 < 2p - 5 + 5
Simplifying the equation gives:
8 < 2p
Step 2: Solve the second inequality: 2p - 5 ≤ 11
Again, add 5 to both sides of the inequality:
2p - 5 + 5 ≤ 11 + 5
Simplifying the equation gives:
2p ≤ 16
Step 3: Divide both sides of the second inequality by 2 to isolate p:
(2p)/2 ≤ 16/2
This simplifies to:
p ≤ 8
Combining the results from Step 1 and Step 3:
8 < 2p and p ≤ 8
The final solution is:
8 < 2p and p ≤ 8
To solve the inequality 3 < 2p - 5 ≤ 11, we need to find the range of values for p that satisfy the inequality.
Let's break this down into two inequalities:
1. 3 < 2p - 5
2. 2p - 5 ≤ 11
1. 3 < 2p - 5
Add 5 to both sides:
3 + 5 < 2p - 5 + 5
8 < 2p
Divide both sides by 2 (since we want to isolate p):
8/2 < 2p/2
4 < p
2. 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
Combining the results from both inequalities, we can state that the solution to the original inequality 3 < 2p - 5 ≤ 11 is: 4 < p ≤ 8.