To solve the inequality \(-2(p - 7) \leq -8\), we will first simplify it step by step.
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Distribute the \(-2\): \[ -2p + 14 \leq -8 \]
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Next, subtract 14 from both sides: \[ -2p \leq -8 - 14 \] \[ -2p \leq -22 \]
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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.
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