Question

Express the interval in​ set-builder notation and graph the interval on a number line.
left parenthesis 7 comma 9 right bracket
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Part 1
Select the correct choice below​ and, if​ necessasry, fill in the answer box to complete your choice.
A.
The solution set in​ set-builder notation is StartSet x vertical line nothing EndSet
  
.
​(Type an inequality or a compound​ inequality.)
B.
The solution set is all real numbers.
C.
There is no solution.

Answer 1

The interval \( (7, 9) \) means that we are considering all the real numbers \( x \) such that \( x \) is greater than 7 and less than 9.

### Part 1: Set-builder notation
The solution set in set-builder notation can be expressed as:
\[
\{ x \mid 7 < x < 9 \}
\]

### Part 2: Graph on a number line
To graph the interval \( (7, 9) \) on a number line:

1. Draw a horizontal line to represent the number line.
2. Mark points for 7 and 9 on the line.
3. Use open circles (not filled in) at both 7 and 9 to indicate that these endpoints are not included in the interval.
4. Shade the region between 7 and 9 to show that all numbers in this range are part of the interval.

This representation visually confirms that \( (7, 9) \) includes all numbers greater than 7 and less than 9, without including 7 or 9 themselves.

### Answer to the options:
The correct choice is:
A. The solution set in set-builder notation is \(\{ x \mid 7 < x < 9 \}\).