We are tasked with solving and graphing the inequality $\frac{x}{3} > -4$.

Step 1: Solve the inequality

To isolate $x$, we can multiply both sides of the inequality by 3 to eliminate the denominator.

$x > -4 \times 3$

$x > -12$

Thus, the solution to the inequality is:

$x > -12$

Step 2: Graph the solution

To graph $x > -12$ on a number line:

1. Draw a number line.
2. Mark the point $-12$ on the line.
3. Use an open circle at $-12$ to indicate that $-12$ is not included in the solution.
4. Shade the region to the right of $-12$, indicating all numbers greater than $-12$.

Graph Explanation:

• The open circle at $-12$ represents that $x = -12$ is not part of the solution.
• The shaded area to the right represents all values greater than $-12$.

Would you like a visual graph for better understanding? Let me know if you have any questions or if you'd like further details.

Here are 5 related questions to expand on this topic:

1. What happens if the inequality was $x/3 \geq -4$?
2. How would the solution change if the inequality was $x/3 < -4$?
3. How would the graph change if the inequality was $x/3 = -4$?
4. What is the solution to $2x + 3 > 7$?
5. How do you graph inequalities involving absolute values?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.