To solve the equation [tex]\(-\frac{1}{5} n + 7 = 2\)[/tex] for [tex]\(n\)[/tex], follow these detailed steps:
1. Start with the given equation:
[tex]\[
-\frac{1}{5} n + 7 = 2
\][/tex]
2. To isolate [tex]\(n\)[/tex], first move the constant term on the left side to the right side by subtracting 7 from both sides:
[tex]\[
-\frac{1}{5} n + 7 - 7 = 2 - 7
\][/tex]
Simplifying this, we get:
[tex]\[
-\frac{1}{5} n = -5
\][/tex]
3. Next, to solve for [tex]\(n\)[/tex], eliminate the fraction by multiplying both sides of the equation by [tex]\(-5\)[/tex]:
[tex]\[
-5 \cdot \left(-\frac{1}{5} n \right) = -5 \cdot (-5)
\][/tex]
Simplifying this, we obtain:
[tex]\[
n = 25
\][/tex]
Thus, the value of [tex]\(n\)[/tex] that makes the equation true is:
[tex]\[
\boxed{25}
\][/tex]
