The question is asking for the set of numbers that are "less than or equal to 4" or "greater than 7."

Let's break this down:

• "Less than or equal to 4" means $x \leq 4$.
• "Greater than 7" means $x > 7$.

So, we are looking for a set where $x \leq 4$ or $x > 7$.

Among the given choices, the correct set notation would be:

$\{x \mid x \leq 4 \text{ or } x > 7\}$

This corresponds to the first option in the image:

$\{x \mid x \leq 4 \text{ or } x > 7\}$

Would you like more details on why this is correct or have any other questions?

Here are 5 related questions:

1. What is the difference between using "or" and "and" in set notation?
2. How would you represent a set of numbers between 3 and 10?
3. What is the set notation for numbers greater than or equal to 5?
4. How would this problem change if the condition was $x \leq 4$ and $x > 7$?
5. How can we graph the solution to this inequality on a number line?

Tip: When dealing with inequalities, always pay attention to whether the symbol is strict ($<$ or $>$) or inclusive ($\leq$ or $\geq$).