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The given inequality is \( 1 < x \leq 6 \). To graph this set and write it in interval notation:

1. **Graphing on the Number Line:**
   - At \( x = 1 \), use an open circle since \( x \) is strictly greater than 1 (it is not included).
   - At \( x = 6 \), use a closed circle since \( x \) is less than or equal to 6 (it is included).
   - Shade the region between 1 and 6 to indicate all the values \( x \) can take.

2. **Interval Notation:**
   The interval notation for the inequality \( 1 < x \leq 6 \) is:
   \[
   (1, 6]
   \]
   - The round bracket \( ( \) indicates that 1 is not included.
   - The square bracket \( ] \) indicates that 6 is included.

Would you like more details or have any questions? 

Here are five related questions you might find useful:
1. What is the difference between strict and non-strict inequalities?
2. How do we graph inequalities with negative numbers?
3. What are the rules for open and closed circles on a number line?
4. How can inequalities be represented in set builder notation?
5. How do we combine multiple inequalities in interval notation?

**Tip:** Always remember that round brackets in interval notation exclude endpoints, while square brackets include them!

Graph the set {x | 1 < x ≤ 6} on the number line. Then, write the set using interval notation.

Learn how to graph the inequality 1 < x ≤ 6 on a number line and write it in interval notation. This problem covers key concepts like inequalities, graphing on the number line, and interval notation, suitable for students in Grades 6-8.

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