The problem is to solve the inequality $1 > z - 8$ and graph the solution on a number line.

1. Problem Description

The problem is to solve the inequality $1 > z - 8$ and graph the solution on a number line.

2. Solution Steps

First, we need to isolate $z$ in the inequality.

To do this, we can add 8 to both sides of the inequality:

$1 + 8 > z - 8 + 8$

$9 > z$

This can also be written as $z < 9$.

So, $z$ is less than

9. This means we need to draw a ray on the number line starting at 9 and extending to the left (towards smaller numbers). Since the inequality is $z < 9$, we should use an open circle at 9, indicating that 9 is not included in the solution.

3. Final Answer

$z < 9$