# What is the solution set for #abs(3x-1) = x+5#?

##### 1 Answer

Aug 5, 2015

#### Explanation:

The first thing that you need to notice here is that the expression on the right side of the equation **must be positive** because it represents the *absolute value* of th expression

So, any solution that does not satisfy the condition

will be an *extraneous solution*.

You need to take into account two possibilities for this equation

#(3x-1)>0# ,*which means that*

#|3x-1| = 3x-1#

and the equation becomes

#(3x-1)<0# ,*which means that*

#|3x-1| = -(3x-1) = -3x + 1#

and the equation becomes

Since both values satisfy the condition