The interval $(- \infty, 7.8)$ represents all real numbers less than 7.8. To express this in set-builder notation, we describe the set of all $x$ values that satisfy this condition. The correct set-builder notation would be:

$\{x \, | \, x < 7.8 \}$

Now, the correct answer for this problem is:

Option A: The solution set in set-builder notation is $\{ x \, | \, x < 7.8 \}$.

Would you like more details on how to graph this interval, or have any further questions?

Here are five related questions to expand on this:

1. How do you graph an interval like $(- \infty, 7.8)$ on a number line?
2. What is the difference between open and closed intervals in interval notation?
3. How would the set-builder notation change if the interval was $[7.8, \infty)$?
4. Can you give an example of a situation where the interval is expressed as $[a, b]$?
5. What does it mean for an interval to be unbounded?

Tip: In interval notation, a parenthesis indicates that an endpoint is not included (open interval), while a bracket indicates that it is included (closed interval).