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The inequality provided is:

\[
-2 \leq 4 - 3a \leq 13
\]

We will solve this compound inequality step by step.

### Step 1: Isolate the middle expression
We want to isolate the variable \( a \) in the middle. To do that, we'll subtract 4 from all parts of the inequality.

\[
-2 - 4 \leq 4 - 3a - 4 \leq 13 - 4
\]

This simplifies to:

\[
-6 \leq -3a \leq 9
\]

### Step 2: Solve for \( a \)
Now, we need to get rid of the coefficient of \( a \), which is \( -3 \). To do that, we divide the entire inequality by \( -3 \). Remember that when dividing by a negative number, we need to flip the inequality signs.

\[
\frac{-6}{-3} \geq \frac{-3a}{-3} \geq \frac{9}{-3}
\]

This simplifies to:

\[
2 \geq a \geq -3
\]

Or written more commonly:

\[
-3 \leq a \leq 2
\]

### Step 3: Graph the solution
The solution is the interval \([-3, 2]\), which means \(a\) is between \(-3\) and \(2\), inclusive of both endpoints.

On the graph:
- Draw a number line.
- Place a solid dot at \( -3 \) and \( 2 \), indicating that \( a \) can be equal to these values.
- Shade the line between these points.

Would you like to clarify any steps or go into more detail?

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Here are 5 related questions to expand on this:

1. How would the solution change if the inequality was \( -2 \leq 4 - 3a < 13 \)?
2. How do we handle inequalities when multiplying or dividing by negative numbers?
3. Can compound inequalities be solved differently if written separately?
4. What is the difference between an open circle and a closed circle in graphing inequalities?
5. How can we verify our solution to this inequality?

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

Learn how to solve and graph the compound inequality -2 ≤ 4 - 3a ≤ 13. This step-by-step solution covers key algebraic concepts like isolating variables and applying the rule of flipping inequalities when dividing by a negative number. Suitable for students in Grades 7-9.

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