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