The inequality in the image is $|w| > 4$. To solve and graph this on the number line, let's break it down:

Step 1: Interpret the inequality

The absolute value inequality $|w| > 4$ means that the value of $w$ is more than 4 units away from 0. Therefore, $w$ could be either:

• Greater than 4 (i.e., $w > 4$), or
• Less than -4 (i.e., $w < -4$).

Step 2: Solution

So the solution to $|w| > 4$ is: $w < -4 \quad \text{or} \quad w > 4$

Step 3: Graph on the number line

1. Plot open circles at $-4$ and $4$ because the inequality is strict ($>$, not $\geq$).
2. Shade to the left of $-4$ and to the right of $4$, indicating that $w$ is either less than $-4$ or greater than $4$.

This is how you would graph the solution on the number line.

Let me know if you'd like any additional details or explanations.

Here are five related questions to practice:

1. How would the graph change if the inequality was $|w| \geq 4$?
2. What would be the solution to $|w| < 3$?
3. How do you solve and graph $|x - 2| > 5$?
4. What are the key differences between solving $|w| > 4$ and $|w| \leq 4$?
5. How do you solve absolute value inequalities that include variables on both sides, like $|2x - 1| > 5$?

Tip: Always remember to use open or closed circles depending on whether the inequality is strict or includes equality!