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Let's solve the compound inequality step by step.

We have two inequalities to solve:

1. \(\frac{m}{3} - 2 \leq -4\)
2. \(3m - 8 > 4\)

### First inequality: \(\frac{m}{3} - 2 \leq -4\)

1. Add 2 to both sides to isolate the \(\frac{m}{3}\):
   \[
   \frac{m}{3} \leq -4 + 2
   \]
   \[
   \frac{m}{3} \leq -2
   \]

2. Multiply both sides by 3 to solve for \(m\):
   \[
   m \leq -2 \times 3
   \]
   \[
   m \leq -6
   \]

### Second inequality: \(3m - 8 > 4\)

1. Add 8 to both sides:
   \[
   3m > 4 + 8
   \]
   \[
   3m > 12
   \]

2. Divide both sides by 3 to solve for \(m\):
   \[
   m > \frac{12}{3}
   \]
   \[
   m > 4
   \]

### Final Answer:
The compound inequality is:
\[
m \leq -6 \quad \text{OR} \quad m > 4
\]

The solution matches the format given:
- \(m \leq -6\) in the first box (green).
- \(m > 4\) in the second box (gray).

Would you like any additional details or further clarification on these steps?

Here are 5 related questions to consider:
1. How do you solve compound inequalities that use "AND" instead of "OR"?
2. What are the key differences between solving equalities and inequalities?
3. How would the inequality change if it included negative coefficients for \(m\)?
4. What do the symbols \(\leq\) and \(>\) mean in terms of graphing the solution on a number line?
5. Can inequalities have infinite solutions, and how can we interpret that?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number!

Solve the following compound inequality: (m / 3) - 2 ≤ -4 OR 3m - 8 > 4.

This step-by-step guide explains how to solve the compound inequality (m / 3) - 2 ≤ -4 OR 3m - 8 > 4. Learn how to isolate variables and apply the addition and multiplication properties of inequalities. This algebra problem is ideal for students in Grades 7-9.

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