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

1 Answer | Add Yours

lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

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:

We’ve answered 333,973 questions. We can answer yours, too.

Ask a question