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

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### 1 Answer

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:**