Expert: Scott A Wilson - 6/11/2010

Question
Im trying to solve for y.
x-1/2y=6
I got stuck when I simplified down to
-1/2y=-1x+6
What did I do wrong? thank you

Answer
Is the equation really x - y/2 = 6?  I prefer writing the denominator after each term.
In this way, when reading the question, it can be seen that it is (1) x - y/2 = 6.
It might be (2) x - 1/(2y) = 6, so that will be answered after the first one.

(1) x - y/2 = 6

In the first step, y was isolated, as it should be, giving -y/2 = -x + 6.

The next thing to do is multiply each term on both sides by -2.

That should give y = 2x - 12, right?

To test this, try putting in, say, x=7 in both equations.

7 - y/2 = 6 turns int0 7-6 = y/2, and that is 1 = y/2, so y=2 is the answer.
Using the answer gives us y = 2(7) - 12 = 14 - 12 = 2, and that is the same as the first.
Since they both agree, it is correct.


Now (1) was probably the right way, since this is Algebra 1, but if not ...

(2) x - 1/(2y) = 6

In the first step the y was isolated, as it should be, giving -1/(2y) = -x + 6.

Of course, if that is it, both sides of -1/(2y) = -x + 6 need to be inverted.

This gives -2y = 1/(-x+6).  Divide both sides by -2 and get y = 1/(-2(-x+6)) = 1/(2x-12).