# How do you solve |x + 2| + 16 = 14?

Jan 8, 2017

See below

#### Explanation:

First, subtract 16 from each side of the equation:

$\left\mid x + 2 \right\mid + 16 - 16 = 14 - 16$

$\left\mid x + 2 \right\mid + 0 = - 2$

$\left\mid x + 2 \right\mid = - 2$

By definition of the absolute value function the result of the function will always be greater than or equal to $0$. Therefore there are no answers for this problem or the solution set is the null set - $x = \left\{\emptyset\right\}$