To solve the equation [tex]\(-\frac{2}{5}(n + 2) = 6\)[/tex], let's proceed step-by-step:
1. Isolate the term involving [tex]\(n\)[/tex] by eliminating the fraction:
[tex]\[
-\frac{2}{5}(n + 2) = 6
\][/tex]
Multiply both sides of the equation by [tex]\(-\frac{5}{2}\)[/tex] to cancel the fractional coefficient on the left side.
[tex]\[
\left( -\frac{2}{5} \right) \times \left( -\frac{5}{2} \right) (n + 2) = 6 \times \left( -\frac{5}{2} \right)
\][/tex]
Simplifying the left side, we get:
[tex]\[
1 \cdot (n + 2) = -15
\][/tex]
So:
[tex]\[
n + 2 = -15
\][/tex]
2. Solve for [tex]\(n\)[/tex]:
[tex]\[
n + 2 = -15
\][/tex]
Subtract 2 from both sides of the equation to isolate [tex]\(n\)[/tex]:
[tex]\[
n = -15 - 2
\][/tex]
[tex]\[
n = -17
\][/tex]
So, the solution for [tex]\(n\)[/tex] is [tex]\(-17\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{D \; n = -17}
\][/tex]
