|3n-6| = 12?

Question

|3n-6|= 12

3n-6=12
3n= 18
n= 6

or

3n+6=12
3n= 6
n= 2

Which is it? Or is it both?

Answer 1

Hi,
The key to working absolute value problems is to realize that the expression inside the absolute value sign can be either negative or positive. For example,
|x| = 7 Then x could be either -7 or 7.
So, to solve your problem we take the term outside the absolute value sign and set it equal to 12 and then -12 and solve for x.
|3n -6| = 12
3n-6 = 12
3n = 12 +6 (Add 6 to each side of the equality.)
3n = 18
n = 6

Now, we must set the expression equal to -12 and solve for x.
3n-6 = -12
3n = -12 + 6 (Add 6 to each side.)
3n = -6
n = -2
Changing the sign of 6 as you did without changing anything on the other side of the equation unbalances the equation.

Hope this helps.
FE

Answer 2

The first one is right. Set 3n - 6 to equal 12 and -12 because you are working with absolute values. Solve those two equations for n. You can do the rest of the work.

Answer 3

we are learning these in class and the first one is set up correctly but the second equation should read: 3n-6= -12
that's negative 12 if you cant tell

Answer 4

3n-6=12
n=6

-(3n-6)=12
-3n+6=12
-3n=6
n=-2