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

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lfryerda eNotes educator | Certified Educator

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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

`2|3n-1|=-1`

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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Student Answers

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. 

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