https://file.aiquickdraw.com/mathbot/file/1729051160598ixkxf7qe.jpg

Let's solve the inequality step by step:

The inequality given is:

\[
|3x + 6| + 5 < 2
\]

### Step 1: Isolate the absolute value
We first isolate the absolute value expression by subtracting 5 from both sides:

\[
|3x + 6| < 2 - 5
\]

This simplifies to:

\[
|3x + 6| < -3
\]

### Step 2: Analyze the inequality
Now, we see that we have the absolute value of an expression being less than a negative number:

\[
|3x + 6| < -3
\]

Since the absolute value of any expression is always non-negative (i.e., \( |A| \geq 0 \) for any \( A \)), it is impossible for an absolute value to be less than a negative number. 

Thus, the inequality has **no solution**.

### Conclusion:
The correct answer is **B**: the solution set is \( \emptyset \) (the empty set).

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How do we solve absolute value inequalities when the right-hand side is positive?
2. Can you give an example of an absolute value inequality that has a solution?
3. What does the solution set represent in this context?
4. How do we express intervals when solving inequalities with absolute values?
5. How would the inequality change if the right-hand side was a positive number?

**Tip:** Always remember that an absolute value expression is never negative, so inequalities comparing absolute values to negative numbers often result in no solution.

Learn how to solve the absolute value inequality |3x + 6| + 5 < 2 with a step-by-step solution. This example highlights the property that absolute values are always non-negative and when inequalities have no solution. Ideal for students in Grades 9-10.

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