https://file.aiquickdraw.com/mathbot/file/1725474011143c7ubu935.jpg

The problem asks you to sketch the region given by the set \(\{(x, y) \mid |x| \leq 4\}\).

### Steps to solve:

1. **Understanding the Inequality**: The inequality \(|x| \leq 4\) means that the \(x\)-coordinate of any point in the region must satisfy this condition. Since \(|x| \leq 4\), this translates to \(-4 \leq x \leq 4\).

2. **Graphing the Region**:
   - The inequality \(-4 \leq x \leq 4\) represents a vertical strip on the graph where the \(x\)-values range between \(-4\) and \(4\).
   - There are no restrictions on the \(y\)-values, so \(y\) can take any value.
   - Therefore, the region consists of all points between the vertical lines \(x = -4\) and \(x = 4\), inclusive of the boundary.

3. **Sketching**:
   - Draw two vertical lines at \(x = -4\) and \(x = 4\).
   - Shade the region between these two lines, extending infinitely in the \(y\)-direction.

This is the graphical representation of the region given by \(\{(x, y) \mid |x| \leq 4\}\).

Do you want any additional details or have any questions?

### Related Questions:

1. What is the graphical representation of \(\{(x, y) \mid |y| \leq 4\}\)?
2. How would the region change if the inequality were strict, i.e., \(|x| < 4\)?
3. What is the interpretation of \(|x + 2| \leq 4\) in terms of graphing?
4. How would you graph the inequality \(\{(x, y) \mid x^2 + y^2 \leq 16\}\)?
5. What does the region look like for the system of inequalities \(|x| \leq 4\) and \(|y| \leq 3\)?

**Tip**: When dealing with absolute value inequalities, it is often helpful to break them down into compound inequalities for easier visualization.

Sketch the region given by the set \(\{(x, y) \mid |x| \leq 4\}\).

Learn how to graph the region defined by the inequality |x| ≤ 4. This problem involves understanding absolute value and inequalities, and is suitable for students in Grades 7-10.

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