https://file.aiquickdraw.com/mathbot/file/1727103249112r5gr12i6.jpg

The inequality provided is:

\[
5 < |w - 3|
\]

### Step-by-Step Solution:

1. Start by solving the absolute value inequality. We know that:
   \[
   |w - 3| > 5
   \]
   This means that:
   \[
   w - 3 < -5 \quad \text{or} \quad w - 3 > 5
   \]

2. Solve each part of the inequality:
   - For \( w - 3 < -5 \):
     \[
     w < -2
     \]
   - For \( w - 3 > 5 \):
     \[
     w > 8
     \]

### Solution:
The solution for \( w \) is:
\[
w < -2 \quad \text{or} \quad w > 8
\]

### Graphing the Solution:
- The solution represents two intervals:
  - From \( -\infty \) to \( -2 \) (open at \( -2 \))
  - From \( 8 \) to \( \infty \) (open at \( 8 \))

On the number line, this would be shown as:
- A ray extending to the left from \( -2 \) with an open circle at \( -2 \).
- Another ray extending to the right from \( 8 \) with an open circle at \( 8 \).

Would you like further details or a specific visual for this graph?

### Follow-up Questions:
1. How would the graph look if the inequality was \( 5 \leq |w - 3| \)?
2. What is the meaning of an "open circle" on a number line in inequality graphs?
3. How would you write the solution in interval notation?
4. What would happen to the solution if the inequality sign was reversed?
5. How can absolute value inequalities be applied in real-life situations?

### Tip:
When solving absolute value inequalities, always consider both the positive and negative cases of the expression inside the absolute value to cover all possible solutions.

Solve for w and graph the solution: 5 < |w - 3|

This lesson demonstrates how to solve the inequality 5 < |w - 3| and graph the solution on a number line. The process covers key algebraic concepts like solving absolute value inequalities and graphing the solution as rays on the number line, with open circles representing excluded endpoints. Suitable for students in Grades 8-10.

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