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

The inequality is:

\[
-2x - 6 \leq 3x - 13 \geq 5
\]

### Step 1: Solve each part of the inequality separately.

#### First inequality: 
\[
-2x - 6 \leq 5
\]

Add 6 to both sides:

\[
-2x \leq 11
\]

Now, divide by -2, remembering to flip the inequality sign:

\[
x \geq -\frac{11}{2} \quad \text{or} \quad x \geq -5.5
\]

#### Second inequality:
\[
3x - 13 \geq 5
\]

Add 13 to both sides:

\[
3x \geq 18
\]

Now divide by 3:

\[
x \geq 6
\]

### Step 2: Combine the results from both inequalities.

The solution is the union of the two results. From the first inequality, \(x \geq -5.5\), and from the second inequality, \(x \geq 6\). 

Since the second inequality \(x \geq 6\) is stricter than the first, the final solution is:

\[
x \geq 6
\]

### Answer: The correct choice is **B**. \(x \geq 6\).

Would you like further clarification or more details?

### Related Questions:
1. How do you solve compound inequalities with "or" and "and"?
2. What happens when you divide or multiply an inequality by a negative number?
3. How do you graph solutions to compound inequalities?
4. How can you verify the solution to a compound inequality?
5. What is the difference between the union and intersection of solutions?

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

Solve the compound inequality: -2x - 6 ≤ 3x - 13 ≥ 5. Select the correct solution from the options provided.

Learn how to solve the compound inequality -2x - 6 ≤ 3x - 13 ≥ 5 step by step, using inequality solving techniques. This problem involves key algebraic concepts, including handling compound inequalities and flipping inequality signs when dividing by a negative number. Suitable for students in Grades 7-10.

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