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

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lfryerda | High School Teacher | (Level 2) Educator

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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


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


`3x-2=-1`  move to right side




Now find the positive argument solution

`3x-2=1`   move to right side




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: