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

1. Problem Description

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

2. Solution Steps

First, we need to isolate $q$ in the inequality. To do this, we add $8$ to both sides of the inequality:

$1 + 8 > q - 8 + 8$

$9 > q$

This inequality can be rewritten as $q < 9$.

This means that $q$ can be any number less than $9$, but not equal to $9$.

To graph the solution on the number line, we need to put an open circle at $9$ since $q$ cannot be equal to $9$. Then we draw an arrow to the left of $9$ to indicate that all values less than $9$ are solutions.

3. Final Answer

The solution to the inequality $1 > q - 8$ is $q < 9$. On the number line, we plot an open circle at 9 and draw an arrow to the left.