We are tasked with solving the inequality:

\[
-\frac{1}{3}(p + 9) \leq 4
\]

### Step 1: Eliminate the fraction by multiplying both sides by \(-3\)

Since we're multiplying by a negative number, we reverse the inequality sign:

\[
p + 9 \geq -12
\]

### Step 2: Solve for \( p \)

Now, subtract 9 from both sides:

\[
p \geq -12 - 9
\]

\[
p \geq -21
\]

### Final Solution:

\[
p \geq -21
\]

So, the solution to the inequality is:

\[
p \geq -21
\]

Would you like more details or have any further questions?

Here are 5 related questions you can explore:
1. How do you solve inequalities that involve absolute values?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. How do you graph the solution \( p \geq -21 \) on a number line?
4. Can inequalities have multiple solutions, and how do you express them?
5. How do you solve compound inequalities?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the inequality -1/3(p + 9) <= 4 by following this step-by-step guide. This problem demonstrates the concept of solving linear inequalities and covers key algebraic techniques. Suitable for students in Grades 7-9.

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