# How do you solve abs(5n-1) = 7?

Sep 27, 2015

See the explanation.

#### Explanation:

$| 5 n - 1 | = 5 n - 1 , 5 n - 1 \ge 0 \iff 5 n \ge 1 \iff n \ge \frac{1}{5}$
$| 5 n - 1 | = - 5 n + 1 , 5 n - 1 < 0 \iff 5 n < 1 \iff n < \frac{1}{5}$

We need to solve 2 equations:
$5 n - 1 = 7 \iff 5 n = 8 \iff n = \frac{8}{5} > \frac{1}{5}$ is a solution
$- 5 n + 1 = 7 \iff - 5 n = 6 \iff n = - \frac{6}{5} < \frac{1}{5}$ is a solution