Question

which of the following is a solution to the inequality below?
$7 < \frac{p}{17} + 11$
$p = -34$
$p = -119$
$p = -68$
$p = -85$

Explanation:

Step1: Solve the inequality for \( p \)

Start with the inequality \( 7 < \frac{p}{17} + 11 \). Subtract 11 from both sides:
\( 7 - 11 < \frac{p}{17} + 11 - 11 \)
\( -4 < \frac{p}{17} \)
Multiply both sides by 17 (since 17 is positive, the inequality sign remains the same):
\( -4\times17 < \frac{p}{17}\times17 \)
\( -68 < p \)
So \( p \) must be greater than -68.

Step2: Check each option

• For \( p = -34 \): \( -34 > -68 \), so this satisfies the inequality.
• For \( p = -119 \): \( -119 < -68 \), so this does not satisfy the inequality.
• For \( p = -68 \): \( -68 = -68 \), but we need \( p > -68 \), so this does not satisfy the inequality.
• For \( p = -85 \): \( -85 < -68 \), so this does not satisfy the inequality.

Answer:

\( p = -34 \)