# How do you solve abs(5n+7)=23?

Sep 8, 2017

The solutions are $S = \left\{- 6 , \frac{16}{5}\right\}$

#### Explanation:

The absolute value is always positive

Therefore,

$| 5 n + 7 | = 23$

$\implies$, $\left(5 n + 7\right) = 23$ and $- \left(5 n + 7\right) = 23$

$5 n = 23 - 7 = 16$, $\implies$, $n = \frac{16}{5}$

and

$5 n + 7 = - 23$, $\implies$, $5 n = - 23 - 7 = - 30$, $\implies$, $n = - 6$