To represent the set \(\{x \mid -2 < x \leq 3\}\) on a number line, follow these steps:

1. **Open interval at \(-2\):** The inequality \(-2 < x\) means that \(x\) can be any value greater than \(-2\), but not equal to \(-2\). This is represented by an **open circle** at \(-2\).
   
2. **Closed interval at \(3\):** The inequality \(x \leq 3\) means that \(x\) can be any value less than or equal to \(3\), including \(3\) itself. This is represented by a **closed circle** at \(3\).

3. **Shade the region:** The values of \(x\) lie between \(-2\) and \(3\), so the region between \(-2\) (not included) and \(3\) (included) will be shaded.

### Number line representation:
- Open circle at \(-2\),
- Closed circle at \(3\),
- The line is shaded between \(-2\) and \(3\).

Would you like further explanation on number line intervals, or have any questions about inequalities?

### 5 Related Questions:
1. How would the set \(\{x \mid -2 \leq x < 3\}\) be represented on the number line?
2. What is the difference between open and closed intervals on a number line?
3. How would you represent the set \(\{x \mid x > 3\}\) on the number line?
4. Can you explain how to convert inequalities into interval notation?
5. How would this inequality change if it included \(x = -2\) as well?

### Tip:
When solving or graphing inequalities, always pay close attention to whether the endpoints are included (closed) or excluded (open).

Learn how to represent the inequality {x | −2 < x ≤ 3} on a number line. This tutorial explains the concept of open and closed intervals and how to visualize inequalities between values. Suitable for students in Grades 6-8.

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