To determine the correct set of possible values for [tex]\( n = 3 \)[/tex], we need to consider the range of integer values from [tex]\(-n\)[/tex] to [tex]\(n\)[/tex], inclusive of zero. In this case, [tex]\( n \)[/tex] is given as 3.
1. Start with the range [tex]\(-n\)[/tex] to [tex]\( n \)[/tex]:
- The given value is [tex]\( n = 3 \)[/tex].
- Thus, the range of possible integer values extends from [tex]\(-3\)[/tex] to [tex]\( 3 \)[/tex].
2. Construct the full set of integers within this range:
- Negative integers: [tex]\(-3, -2, -1\)[/tex].
- Zero: [tex]\(0\)[/tex].
- Positive integers: [tex]\(1, 2, 3\)[/tex].
Combining these, the complete set of numbers is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Therefore, the correct set of possible values for [tex]\( n = 3 \)[/tex] is:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]
This corresponds to the fourth option listed in the question. Hence, the right choice is:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]
