To solve the problem of finding the value of [tex]\(7 + \frac{1}{2} n\)[/tex] rounded to the nearest whole number when [tex]\(-2 < n < -1\)[/tex], we can follow these steps:
1. Determine a representative value for [tex]\( n \)[/tex]: Since [tex]\( n \)[/tex] lies between [tex]\(-2\)[/tex] and [tex]\(-1\)[/tex], we can choose a midpoint value to evaluate the expression more conveniently. The midpoint is [tex]\(\frac{-2 + (-1)}{2}\)[/tex], which simplifies to [tex]\(-1.5\)[/tex].
2. Substitute and calculate: Substitute [tex]\( n = -1.5 \)[/tex] into the expression [tex]\(7 + \frac{1}{2} n\)[/tex].
[tex]\[
7 + \frac{1}{2} (-1.5) = 7 + \left(-0.75 \right) = 7 - 0.75 = 6.25
\][/tex]
3. Round to the nearest whole number: Finally, round the result of [tex]\(6.25\)[/tex] to the nearest whole number. When rounding, we know that if the decimal part is 0.5 or greater, we round up, and if it's less than 0.5, we round down.
[tex]\[
6.25 \text{ rounded to the nearest whole number is } 6
\][/tex]
Therefore, the value of [tex]\(7 + \frac{1}{2} n\)[/tex] rounded to the nearest whole number, when [tex]\(-2 < n < -1\)[/tex], is [tex]\(6\)[/tex].
