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What value of [tex]$n$[/tex] makes the equation true?
[tex]\[
-\frac{1}{5} n + 7 = 2
\][/tex]

[tex]n = \square[/tex]


Sagot :

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]