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.