The inequality given is:

\[
20 > -4x \geq -8
\]

This is a compound inequality, and we need to solve it step by step. First, split it into two parts:

1. \( 20 > -4x \)
2. \( -4x \geq -8 \)

### Solving the first part:
\[
20 > -4x
\]
To isolate \(x\), divide both sides by \(-4\). Remember to **flip the inequality** sign when dividing by a negative number:

\[
\frac{20}{-4} < x \implies -5 < x
\]

### Solving the second part:
\[
-4x \geq -8
\]
Again, divide both sides by \(-4\), flipping the inequality sign:

\[
x \leq \frac{-8}{-4} \implies x \leq 2
\]

### Final solution:
Now, combining both results:

\[
-5 < x \leq 2
\]

The solution set is \(x\) in the interval \((-5, 2]\).

Would you like more details or have any questions?

Here are some related questions you might consider:
1. How do you solve inequalities with fractions?
2. How do compound inequalities work with three parts?
3. What happens if both sides of the inequality are divided by a negative number?
4. How would the solution change if the inequality were \( \geq \) instead of \( > \)?
5. Can inequalities have infinite solutions?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the compound inequality 20 > -4x ≥ -8 with a clear, step-by-step explanation. This solution covers key algebraic concepts including how to divide inequalities by negative numbers and apply inequality rules. Perfect for Grades 7-9 students.

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