Solve this equation if possible. `-3|6n-2|+5=8`
2 Answers
lfryerda | High School Teacher | (Level 2) Educator
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.
jakx789 | Student, Undergraduate | (Level 1) eNoter
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.