To solve the problem shown in the image, let's break it down into two parts: graphing the set on the number line and writing the set using interval notation.

Graphing the Set

The set given is $\{ x \mid -5 < x < -2 \}$. This means we need to graph all the values of $x$ that are greater than $-5$ and less than $-2$.

1. Identify $-5$ and $-2$ on the number line.
2. Since the inequalities are strict (i.e., $x$ is not equal to $-5$ and $-2$), we will use open circles at $-5$ and $-2$ to indicate that these points are not included in the set.
3. Draw a line connecting the open circles to represent all the numbers between $-5$ and $-2$.

Interval Notation

Interval notation for the set $\{ x \mid -5 < x < -2 \}$ is written as: $(-5, -2)$

Here, parentheses are used instead of brackets to denote that the endpoints $-5$ and $-2$ are not included in the set.

Answer Summary

• Graph: Draw a number line with open circles at $-5$ and $-2$, with a line segment connecting them.
• Interval Notation: $(-5, -2)$

Example Diagram

If we were to visualize it, the number line would look like this:

-7  -6  -5  -4  -3  -2  -1  0   1
    (---------o---------o---------)

Where the open circles at $-5$ and $-2$ indicate those points are