How do you solve abs(2n-5)=7?

May 9, 2018

The answer to the problem is $n = 6 \text{ and } n = - 1$

Explanation:

With absolute value, you'll have two answers; one of them assuming $2 n - 5$ is positive and one assuming $2 n - 5$ is negative.

Therefore, we have to set it up like this:

$2 n - 5 = 7$

$2 n - 5 = - 7$

We set it up like this because $\left\mid 7 \right\mid$ and $\left\mid - 7 \right\mid$ both equal $7$.

We can solve both equations pretty easily:

$2 n - 5 = 7$
$2 n = 12$
$n = \textcolor{red}{6}$

$2 n - 5 = - 7$
$2 n = - 2$
$n = \textcolor{red}{- 1}$