The question asks to identify the set of all real numbers greater than 11 and less than 32 in set-builder notation. Set-builder notation represents the set by describing the properties that its elements must satisfy.

In this case, the correct description should be $x$, where $11 < x < 32$, meaning $x$ is a real number between 11 and 32. Let's examine the options provided in the image:

1. $\{ x \mid 9 \leq x \leq 102 \}$
2. $\{ x \mid 11 < x < 32 \}$
3. $\{ x \mid 10 \leq x \leq 50 \}$
4. $\{ x \mid 12 < x < 52 \}$

The second option, $\{ x \mid 11 < x < 32 \}$, correctly matches the requirement of finding real numbers greater than 11 and less than 32.

Do you want further explanation or have any questions?

Here are five related questions to expand your understanding:

1. How do we use interval notation to represent the same set of real numbers?
2. What is the difference between strict inequalities (e.g., $<$) and non-strict inequalities (e.g., $\leq$) in set-builder notation?
3. How would you represent the same set of numbers on a number line?
4. What does the union of two sets look like in set-builder notation?
5. How can you express the complement of the set $\{ x \mid 11 < x < 32 \}$ in set-builder notation?

Tip: When converting between set-builder and interval notation, remember that parentheses ( $()$ ) indicate strict inequality ( $<$ ), while brackets ( $[]$ ) indicate inclusive inequality ( $\leq$ ).