# How do you solve the equation abs(x+a)=b?

Aug 24, 2017

See a solution process below:

#### Explanation:

Assuming solving the equation for $x$:

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.

Solution 1:

$x + a = - b$

$x + a - \textcolor{red}{a} = - b - \textcolor{red}{a}$

$x + 0 = - b - a$

$x = - b - a$

Solution 2:

$x + a = b$

$x + a - \textcolor{red}{a} = b - \textcolor{red}{a}$

$x + 0 = b - a$

$x = b - a$

The Solutions Are:

$x = - b - a$ and $x = b - a$

Or

$x = \pm b - a$