We are tasked with solving the absolute value inequality:

$|5x + 4| < -6$

Step 1: Analyze the inequality

First, recognize that the absolute value of any expression is always non-negative (i.e., it is always greater than or equal to 0). Therefore, it can never be less than a negative number. Here, the right-hand side of the inequality is -6, a negative number.

$|5x + 4| \geq 0 \quad \text{for all values of } x$

Since the inequality is asking whether an absolute value expression can be less than a negative number (which is impossible), there is no solution to this inequality.

Step 2: Conclusion

The solution is the empty set.

Thus, the correct answer is:

$\text{B. The solution is the empty set.}$

Step 3: Graph the solution

Since there is no solution, the graph on a real number line would be empty—there are no values of $x$ that satisfy this inequality.

---

Do you want more details, or have any questions about this?
Here are 5 related questions that expand on this concept:

1. What happens when the inequality involves $|5x + 4| \leq 6$?
2. How would the solution change if the right side were a positive number, like 6?
3. How do we solve inequalities involving $|5x + 4| > 6$?
4. How can we graph an absolute value inequality on a number line for different cases?
5. What are the properties of absolute value functions?

Tip: Absolute value inequalities involving a negative number on the right side often have no solutions because absolute values are always non-negative.