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Solve this equation if possible. `-3|6n-2|+5=8` 

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lfryerda eNotes educator | Certified Educator

calendarEducator since 2012

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To solve the absolute value equation, we try and simplify the equation first:

`-3|6n-2|+5=8`   move 5 to other side

`-3|6n-2|=3`   divide both sides by -3

`|6n-2|=-1`   factor 2 from left side


Unfortunately, since the left side of this equation is always positive and the right side of the equation is always negative, we see that the equation has no solution.

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jakx789 | Student

okay so we get the absolute value on one side only so we have 

abs(6n-2) = -1

since (8-5)/-3 = -1

then, we split this into two equations because we are dealing with absolute values so one equation is

1)6n-2= -1

and the second is

2) 6n-2 = +1

then we solve for both.

This is what we would normally do. However, notice how abs(6n-2) can't possibly equal a negative number. Therefore, this problem has no solution. If you would like to see, solve for 1) and 2) and notice how you get

n= 1/2 

and n = 1/6

However, plugging these numbers into the original equation does not give a solution.

Hence, this problem has no solution.