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

1. Problem Description

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

2. Solution Steps

To solve the inequality $1 > z - 8$, we need to isolate the variable $z$. We can do this by adding $8$ to both sides of the inequality:

$1 + 8 > z - 8 + 8$

$9 > z$

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

The solution to the inequality is all values of $z$ that are less than $9$. To graph this on a number line, we need to place an open circle at $9$ to indicate that $9$ is not included in the solution set, and then draw an arrow extending to the left, indicating that all values less than $9$ are part of the solution.

3. Final Answer

$z < 9$