# How do you solve abs(x-16)<10?

Nov 15, 2017

See a solution process below:

#### Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

$- 10 < x - 16 < 10$

First, add $\textcolor{red}{16}$ to each segment of the system of inequalities to solve for $x$ while keeping the system balanced:

$- 10 + \textcolor{red}{16} < x - 16 + \textcolor{red}{16} < 10 + \textcolor{red}{16}$

$6 < x - 0 < 26$

$6 < x < 26$

Or

$x > 6$ and $x < 26$

Or, in interval notation

$\left(6 , 26\right)$