To solve the inequality [tex]\(\frac{p}{-2} + 25 \geq -5\)[/tex], follow these steps:
1. Isolate the term with [tex]\(p\)[/tex] on one side of the inequality:
[tex]\[
\frac{p}{-2} \geq -5 - 25
\][/tex]
This involves subtracting 25 from both sides:
[tex]\[
\frac{p}{-2} \geq -30
\][/tex]
2. Clear the fraction by multiplying both sides by -2:
When you multiply or divide by a negative number in an inequality, the direction of the inequality sign reverses:
[tex]\[
p \leq -30 \times -2
\][/tex]
3. Simplify the right-hand side:
[tex]\[
p \leq 60
\][/tex]
Thus, the final answer is:
[tex]\[
p \leq 60
\][/tex]
So, the correct option is (C) [tex]\(p \leq 60\)[/tex].
