https://file.aiquickdraw.com/mathbot/file/17295545497265gn5ozzz.jpg

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!

|w| > 4. Graph the solution to the inequality on the number line.

Learn how to solve and graph the absolute value inequality |w| > 4 on a number line. This problem demonstrates key concepts in inequalities and absolute values, suitable for students in Grades 7-9.

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