https://file.aiquickdraw.com/mathbot/file/1727187791268e63cf0zd.jpg

Let's solve the given compound inequality step by step:

### Compound inequality:
\[
2x - 3 \geq -11 \quad \text{and} \quad 2x + 6 \leq 8
\]

#### Step 1: Solve each inequality separately.

1. **For \(2x - 3 \geq -11\):**

   Add 3 to both sides:
   \[
   2x \geq -11 + 3
   \]
   \[
   2x \geq -8
   \]

   Now, divide both sides by 2:
   \[
   x \geq -4
   \]

2. **For \(2x + 6 \leq 8\):**

   Subtract 6 from both sides:
   \[
   2x \leq 8 - 6
   \]
   \[
   2x \leq 2
   \]

   Now, divide both sides by 2:
   \[
   x \leq 1
   \]

#### Step 2: Combine the inequalities.

The solution to the compound inequality is:
\[
-4 \leq x \leq 1
\]

### Step 3: Graph the solution on the number line.

The solution represents all values of \(x\) between \(-4\) and \(1\), inclusive of \(-4\) and \(1\) since both inequalities are non-strict (they include the equal sign).

The graph would show a closed dot at \(x = -4\) and another closed dot at \(x = 1\), with a line connecting these points.

Would you like me to plot this on a number line?

### Related questions:
1. What is the difference between a strict and a non-strict inequality?
2. How do you solve compound inequalities involving "or" instead of "and"?
3. Can compound inequalities have no solution?
4. How do you graph solutions to compound inequalities with fractions?
5. What happens if we reverse both inequalities?

**Tip:** Always check if the inequality sign flips when dividing or multiplying by a negative number.

Solve the compound inequality: 2x - 3 ≥ -11 and 2x + 6 ≤ 8. Graph the solution on the number line.

Learn how to solve the compound inequality 2x - 3 ≥ -11 and 2x + 6 ≤ 8 with a detailed step-by-step solution. This problem involves key algebraic concepts and inequalities, suitable for students in Grades 8-10. Graphical representation of the solution is included.

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