Let's determine the set of possible values for [tex]\( n = 3 \)[/tex].
First, consider what it means for a number to be included in this set. Since [tex]\( n \)[/tex] is set to 3, we need the set of numbers that ranges from [tex]\(-n\)[/tex] to [tex]\( n \)[/tex]. Specifically, we are looking for all integer values from [tex]\(-3\)[/tex] to [tex]\( 3 \)[/tex].
Step-by-step, let's identify the values in this range:
1. Start at [tex]\(-3\)[/tex].
2. Move to the next integer: [tex]\(-2\)[/tex].
3. Continue to the next integer: [tex]\(-1\)[/tex].
4. Continue to the next integer: [tex]\(0\)[/tex].
5. Continue to the next integer: [tex]\(1\)[/tex].
6. Continue to the next integer: [tex]\(2\)[/tex].
7. Finally, include the upper limit: [tex]\(3\)[/tex].
Putting all these values together, the complete set is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Therefore, the set of numbers that gives the correct possible values for [tex]\( n = 3 \)[/tex] is:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]
Hence, the correct choice is:
[tex]\[ \boxed{-3, -2, -1, 0, 1, 2, 3} \][/tex]
