Question

Express the interval in​ set-builder notation and graph the interval on a number line.
left parenthesis 6 comma infinity right parenthesis
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set in​ set-builder notation is StartSet x vertical line nothing EndSet
  
.
​(Use integers or fractions for any numbers in the​ expression.)
B.
The solution set is all real numbers.
C.
There is no solution.

Answer 1

To express the interval \( (6, \infty) \) in set-builder notation, we describe the set of all \( x \) such that \( x \) is greater than 6.

**Part 1: Set-Builder Notation**

The correct answer is:

A. The solution set in set-builder notation is \(\{ x \mid x > 6 \}\).

**Part 2: Graphing on a Number Line**

To graph the interval \( (6, \infty) \):
1. Draw a number line.
2. Locate the point at 6.
3. Place an open circle at 6 to indicate that 6 is not included in the interval.
4. Shade the line to the right of 6 to indicate that the interval continues indefinitely in that direction.

Here is a visual representation of how you might draw this:

```
|-------------o====================>
| 6
```

The open circle at 6 shows that 6 is not included, and the shaded line to the right indicates all numbers greater than 6 are part of the set.