Certainly! Let's solve the equation step-by-step.
We start with the given equation:
[tex]\[ -\frac{2}{5}(n + 2) = 6 \][/tex]
### Step 1: Isolate the expression containing [tex]\( n \)[/tex]
First, we need to eliminate the fraction by multiplying both sides of the equation by the reciprocal of [tex]\(-\frac{2}{5}\)[/tex], which is [tex]\(-\frac{5}{2}\)[/tex]:
[tex]\[ \left(-\frac{5}{2}\right) \times \left( -\frac{2}{5}(n + 2) \right) = 6 \times \left(-\frac{5}{2}\right) \][/tex]
Simplifying the left-hand side:
[tex]\[ (n + 2) = 6 \times \left(-\frac{5}{2}\right) \][/tex]
### Step 2: Simplify the right-hand side
Calculate the multiplication on the right-hand side:
[tex]\[ 6 \times \left(-\frac{5}{2}\right) = -15 \][/tex]
So the equation now becomes:
[tex]\[ n + 2 = -15 \][/tex]
### Step 3: Solve for [tex]\( n \)[/tex]
To isolate [tex]\( n \)[/tex], subtract 2 from both sides:
[tex]\[ n + 2 - 2 = -15 - 2 \][/tex]
[tex]\[ n = -17 \][/tex]
So, the solution to the equation [tex]\( -\frac{2}{5}(n + 2) = 6 \)[/tex] is:
[tex]\[ n = -17 \][/tex]
### Conclusion
Thus, the correct answer is:
[tex]\[ \boxed{-17} \][/tex]
