Solve this equation if possible. `-3|6n-2|+5=8`
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.
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
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
and n = 1/6
However, plugging these numbers into the original equation does not give a solution.
Hence, this problem has no solution.