To solve the inequality [tex]\(\frac{3}{4} p + 8 \geq 3\)[/tex], let's go through the solution step-by-step:
1. Start with the given inequality:
[tex]\[\frac{3}{4} p + 8 \geq 3\][/tex]
2. Subtract 8 from both sides to isolate the term with [tex]\(p\)[/tex] on the left side:
[tex]\[\frac{3}{4} p + 8 - 8 \geq 3 - 8\][/tex]
Simplifying this, we get:
[tex]\[\frac{3}{4} p \geq -5\][/tex]
3. Next, to isolate [tex]\(p\)[/tex], we need to get rid of the fraction. We can do this by multiplying both sides of the inequality by the reciprocal of [tex]\(\frac{3}{4}\)[/tex], which is [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[\frac{4}{3} \cdot \frac{3}{4} p \geq -5 \cdot \frac{4}{3}\][/tex]
Simplifying this, we get:
[tex]\[p \geq -\frac{20}{3}\][/tex]
4. Thus, the solution to the inequality is:
[tex]\[p \geq -\frac{20}{3}\][/tex]
From the given answer choices, the correct one is:
[tex]\[p \geq -\frac{20}{3}\][/tex]
