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

Mar 5, 2016

In absolute value equations, there are two scenarios that you must consider and therefore there will be two solutions

#### Explanation:

Scenario 1: The absolute value is positive:

$3 - x = 6$

$- x = 3$

$x = - 3$

Scenario 2: The absolute value is negative:

$- \left(3 - x\right) = 6$

#-3 + x = 6

$x = 9$

Always check your solutions in the original equation. Both solutions work, so the solution set is $\left\{x = - 3 , 9\right\}$

Hopefully this helps.