To determine the correct set of possible values for [tex]\( n = 3 \)[/tex], we need to thoroughly understand which numbers can be included for the given [tex]\( n \)[/tex].
Given [tex]\( n = 3 \)[/tex], we should consider all the integers starting from [tex]\(-n\)[/tex] to [tex]\( n \)[/tex]. Let's list them step by step:
1. The value of [tex]\( n = 3 \)[/tex].
2. Consider all integers between [tex]\(-n\)[/tex] and [tex]\( n \)[/tex], inclusive.
3. Therefore, we start from [tex]\(-3\)[/tex] and move incrementally to the right up to [tex]\( 3 \)[/tex].
The integers in this range are:
- [tex]\(-3\)[/tex]
- [tex]\(-2\)[/tex]
- [tex]\(-1\)[/tex]
- [tex]\(0\)[/tex]
- [tex]\(1\)[/tex]
- [tex]\(2\)[/tex]
- [tex]\(3\)[/tex]
So, the complete set of possible values for [tex]\( n = 3 \)[/tex] is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Thus, the correct set of numbers in the choice list given by the possible values for [tex]\( n = 3 \)[/tex] is:
[tex]\(\boxed{-3,-2,-1,0,1,2,3}\)[/tex]
