What is the sum of the solution of 2|3x-2|-6=-4? Graph the solution 

Expert Answers
lfryerda eNotes educator| Certified Educator

Since this is an equation of absolute values, then there will either be two solutions or no solutions.  To determine the solutions, we simplify algebraically first:

`2|3x-2|-6=-4`   move -6 to right side

`2|3x-2|=-4+6`   simplify

`2|3x-2|=2`   divide by 2

`|3x-2|=1`

Now there are two different equations.  Find the value when the absolute value argument is negative and when it is positive.

`-(3x-2)=1`

`3x-2=-1`  move to right side

`3x=-1+2`

`3x=1`

`x=1/3`

Now find the positive argument solution

`3x-2=1`   move to right side

`3x=1+2`

`3x=3`

`x=1`

There are two solutions x=1 and x=1/3, so the sum of the solutions is `1+1/3=4/3` .  The graph of the solutions is: