From the image, it appears the problem asks to graph the solution for the inequality $|w| < 8$. Let's analyze and solve it correctly.

Steps to Solve:

1. Understand Absolute Value Inequality:

   • The inequality $|w| < 8$ means the values of $w$ are within 8 units from 0. In mathematical terms, this translates to: $-8 < w < 8$
   • This indicates an open interval where $w$ lies between $-8$ and $8$ (excluding $-8$ and $8$).

2. Graph Representation:

   • On the number line, the solution should be represented as a line segment between $-8$ and $8$ with open circles at $-8$ and $8$, since the values at these points are not included in the solution.

Issue in the Uploaded Graph:

The graph shown in your response incorrectly represents the inequality $|w| < 8$. Instead, it seems to be incorrectly marking the range from $8$ to a larger value, or the setup is not consistent with the correct representation of the inequality.

Correct Graph:

• On the number line, draw a line segment starting just after $-8$ and ending just before $8$.
• Use open circles (not filled) at $-8$ and $8$.

Would you like me to generate a clean and clear image of the correct graph? Let me know if you have any questions or would like further clarification.

Follow-up Questions:

1. Why is it necessary to use open circles for $-8$ and $8$?
2. How would the graph change if the inequality were $|w| \leq 8$?
3. How do absolute value inequalities translate into compound inequalities?
4. Can you explain why the solution excludes $w = -8$ and $w = 8$?
5. What does the inequality $|w| > 8$ look like on a graph?

Tip:

When solving absolute value inequalities, always rewrite them into equivalent compound inequalities for clarity before graphing.