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!