Let's solve the inequality step by step.

We are given:
\[
-20 \leq -4x - 4 \quad \text{or} \quad -4x - 4 \leq -44
\]

### First Inequality: \(-20 \leq -4x - 4\)

1. Add \(4\) to both sides:
   \[
   -20 + 4 \leq -4x
   \]
   \[
   -16 \leq -4x
   \]

2. Divide both sides by \(-4\). Remember, when dividing by a negative number, the inequality sign flips:
   \[
   \frac{-16}{-4} \geq \frac{-4x}{-4}
   \]
   \[
   4 \geq x
   \]
   This simplifies to:
   \[
   x \leq 4
   \]

### Second Inequality: \(-4x - 4 \leq -44\)

1. Add \(4\) to both sides:
   \[
   -4x \leq -44 + 4
   \]
   \[
   -4x \leq -40
   \]

2. Divide both sides by \(-4\), flipping the inequality sign:
   \[
   \frac{-4x}{-4} \geq \frac{-40}{-4}
   \]
   \[
   x \geq 10
   \]

### Final Solution

The solution is the union of the two inequalities:
\[
x \leq 4 \quad \text{or} \quad x \geq 10
\]

So, the solution is:
\[
x \in (-\infty, 4] \cup [10, \infty)
\]

Would you like more details on any part of the process?

Here are 5 related questions:
1. How do you solve inequalities involving fractions?
2. What happens if we multiply both sides of an inequality by a negative number?
3. How do you solve systems of inequalities?
4. What is the difference between solving a compound inequality and a regular one?
5. How do we graph the solution to a compound inequality on a number line?

**Tip**: When dividing or multiplying an inequality by a negative number, always remember to flip the inequality sign!

−20 ≤ −4x − 4 or −4x − 4 ≤ −44

Learn how to solve the compound inequality −20 ≤ −4x − 4 or −4x − 4 ≤ −44 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequality manipulation and solving linear equations, and is suitable for students in Grades 8-10.

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