The correct graph for the solution $x < -\frac{4}{3}$ is:

• A number line with an open parenthesis at $-\frac{4}{3}$, indicating that $-\frac{4}{3}$ is not included in the solution set.
• The region to the left of this point should be shaded, representing all values less than $-\frac{4}{3}$.

Given these criteria, the correct answer is:

A. A number line is labeled from negative 15 to 0 in increments of 1. The region to the left of a right parenthesis at negative four-thirds is shaded.

Would you like any further details or have any questions?

Here are 5 related questions for further exploration:

1. How would the graph look if the inequality was $x \leq -\frac{4}{3}$?
2. How does the graph change if the inequality is $x > -\frac{4}{3}$?
3. What does an open circle or parenthesis on a number line represent?
4. How can you check if a specific number is part of the solution set?
5. What happens to the graph if the inequality flips to $x > \frac{4}{3}$?

Tip: An open parenthesis or circle on a graph indicates that the endpoint is not included in the solution set.