Math Questions and Answers

Start Your Free Trial

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

Expert Answers info

lfryerda eNotes educator | Certified Educator

calendarEducator since 2012

write738 answers

starTop subjects are Math and Science

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:

check Approved by eNotes Editorial