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).