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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).

Express the interval (-∞, 7.8) in set-builder notation and select the correct answer from the choices provided.

Learn how to express the interval (-∞, 7.8) in set-builder notation. This problem introduces the concept of inequalities and interval notation, suitable for students in Grades 8-10.

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