https://file.aiquickdraw.com/mathbot/file/1727356704713hv0ep4go.jpg

Let's break down and solve the problem from the image:

1. **Part a)**: The number \( n \) is less than 12.  
   The inequality representing this is:  
   \[
   n < 12
   \]

2. **Part b)**: The number \( n \) is more than 8.  
   The inequality representing this is:  
   \[
   n > 8
   \]

3. **Part c)**: Drawing these inequalities on a number line.  
   To represent \( 8 < n < 12 \) on a number line, we would have an open circle at 8 (not including 8) and an open circle at 12 (not including 12), with a line connecting the two open circles.

4. **Part d)**: The possible values of \( n \) (since \( n \) is an integer) are the integers between 8 and 12.  
   So, the possible values are:  
   \[
   n = 9, 10, 11
   \]

Would you like me to sketch the number line for you? Let me know if you'd like further details or have any questions!

Here are 5 related questions for practice:
1. What inequality would represent a number being more than 5 but less than or equal to 15?
2. Can a value of \( n = 8 \) be included in this set?
3. How would the inequality change if the number was less than or equal to 12?
4. What would the possible integer values of \( n \) be if \( n > 3 \) and \( n < 7 \)?
5. How does the solution change if \( n \) is not restricted to integers?

**Tip**: When drawing inequalities on a number line, open circles indicate values that are *not included*, while closed circles represent values that *are included*.

I think of an integer, n.

a) My number is less than 12. Write an inequality to show this.
b) My number is more than 8. Write an inequality to show this.
c) Draw both of these inequalities on a number line.
d) What are the possible values of my number?

Learn how to represent inequalities on a number line and find the possible integer values for a number greater than 8 and less than 12. This problem is suitable for Grades 6-8 and covers key concepts in inequalities and number line representation.

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