Question

-2(Given the inequality below, which statement is true?


Question 8 options:

-11 is the minimum value of p


11 is the maximum value of p


-11 is the maximum value of p


11 is the minimum value of p

-2(p-7) \leq -8

Answer 1

To solve the inequality \(-2(p - 7) \leq -8\), we will first simplify it step by step.

1. Distribute the \(-2\):
\[
-2p + 14 \leq -8
\]

2. Next, subtract 14 from both sides:
\[
-2p \leq -8 - 14
\]
\[
-2p \leq -22
\]

3. Now, divide both sides by \(-2\). Remember that dividing or multiplying by a negative number reverses the inequality sign:
\[
p \geq 11
\]

From this result, we can see that \(p\) has a minimum value of \(11\) (it can be equal to \(11\) or greater).

Given the options:

- **-11 is the minimum value of p**
- **11 is the maximum value of p**
- **-11 is the maximum value of p**
- **11 is the minimum value of p**

The correct statement is:

**11 is the minimum value of p.**