|7/5x - 12|=3

Suppose the question was |N| = 3

Then N could be 3 because |3| is 3, or N could be -3 because |-3| is 3.

Now replace N by 7/5x - 12.

I think there is actually two solutions here.

|7/5x - 12|=3

(7/5x +12) = 3

          -12     -12

7/5x = -9

7x = 9*5

7x=45

x = 45/7

|7/5x - 12|=3

|7/5x| = 15

7/5x = 15

7x = 15*5

7x=75

x=75/7

I'm not sure what the correct explanation is, but I'm pretty sure that's the answer.

Can anyone explain the "proper" way to do this?

Notice that absolute value of a number n is = n if n > 0   and -n if n < 0.

And note that l3l = 3   and l-3l = 3

This implies that

(7/5x - 12) = 3       and  (7/5x - 12) = -3

Solving the first equation, we have

7x - 60 = 15

7x= 75

x = 75/7

And solving the second equation, we have

7x - 60 = -15

7x = 45

x = 45/7

Just as NinjaDevo found !!!!

That kind-of makes sense. I get why you can do

(7/5x - 12) = 3

but why can you do

(7/5x - 12) = -3 ?

You lost me there...