The problem is to solve the inequality $3 \le h - 6$ and graph the solution on a number line.

1. Problem Description

The problem is to solve the inequality $3 \le h - 6$ and graph the solution on a number line.

2. Solution Steps

To solve the inequality $3 \le h - 6$, we want to isolate $h$ on one side of the inequality. We can do this by adding 6 to both sides of the inequality.

$3 \le h - 6$

$3 + 6 \le h - 6 + 6$

$9 \le h$

This can also be written as $h \ge 9$.

To graph the solution $h \ge 9$, we need to draw a ray on the number line starting at 9 and extending to the right. Since the inequality is $h \ge 9$, the endpoint at 9 should be a closed circle, indicating that 9 is included in the solution. The ray extends to the right, indicating that all values greater than 9 are also part of the solution.

3. Final Answer

$h \ge 9$. The solution is a closed ray starting at 9 and going to the right.