# How do you solve #x+3=-abs(3x-1)#?

##### 1 Answer

Consider two possibilities which are significant for the absolute value term

**Possibility 1:**

In this case

and the equation can be re-written

Note that this is an extraneous solution since it does not exist within the range of values for Possibility 1:

**Possibility 2:

In this case

and the equation can be re-written

Note that once again we have an extraneous solution sin it does not exist within the range of values for Possibility 2: (

To see why this happens consider a re-arrangement of the original equation into the form:

The graph of the left side of this equation is shown below. Notice that it does not intersect the X-axis (that is it is never equal to

graph{x+3+abs(3x-1) [-16.01, 16.02, -8.01, 8]}