# How do you solve abs(x-3)-6=2?

Mar 14, 2018

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{6}$ to each side of the equation to isolate the absolute value function while keeping the equation balanced:

$\left\mid x - 3 \right\mid - 6 + \textcolor{red}{6} = 2 + \textcolor{red}{6}$

$\left\mid x - 3 \right\mid - 0 = 8$

$\left\mid x - 3 \right\mid = 8$

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:

$x - 3 = - 8$

$x - 3 + \textcolor{red}{3} = - 8 + \textcolor{red}{3}$

$x - 0 = - 5$

$x = - 5$

Solution 2:

$x - 3 = 8$

$x - 3 + \textcolor{red}{3} = 8 + \textcolor{red}{3}$

$x - 0 = 11$

$x = 11$

The Solution Set Is:

x = {-5, 11}

Mar 14, 2018

{x-3>0
{-x+3>0#

So it's either $x - 3$ or $- x + 3$ and you put both of these separate

$x - 3 - 6 = 2$ from where $x = 11$

and

$- x + 3 - 6 = 2$ from where $x = - 5$