Choose the correct graph below. 

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.-1500

font size decreased by 3 negative four thirds . nbsp−43.  

B.

A number line is labeled from negative 15 to 0 in increments of 1. The region to the right of a left bracket at negative four thirds is shaded.-1500

font size decreased by 3 negative four thirds . nbsp−43.  

C.

A number line is labeled from negative 15 to 0 in increments of 1. The region to the right of a left parenthesis at negative four thirds is shaded.-1500

font size decreased by 3 negative four thirds . nbsp−43.  

D.

A number line is labeled from negative 15 to 0 in increments of 1. The region to the left of a right bracket at negative four thirds is shaded.-1500

font size decreased by 3 negative four thirds . nbsp−43.  

E.

A number line is labeled from negative 15 to 0 in increments of 1.-1500

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.

Explore how to choose the correct graph representation for inequalities on a number line. This problem covers key concepts including inequalities, number line shading, and graph interpretation. Suitable for students in Grades 7-9.

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