# How do you solve abs(-x+9)=4?

Mar 13, 2018

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.

Solution 1:

$- x + 9 = - 4$

$- x + \textcolor{red}{x} + 9 + \textcolor{red}{4} = - 4 + \textcolor{red}{4} + \textcolor{red}{x}$

$0 + 13 = 0 + x$

$13 = x$

$x = 13$

Solution 2:

$- x + 9 = 4$

$- x + \textcolor{red}{x} + 9 - \textcolor{red}{4} = 4 - \textcolor{red}{4} + \textcolor{red}{x}$

$0 + 5 = 0 + x$

$5 = x$

$x = 5$

The Solution Set Is: $x = \left\{5 , 13\right\}$