Answer: Y

Step 2: Get “y” on one side and everything else on the other.

Step 2a: Take care of the two first. To isolate “Y” on the left of the equation, add two to both sides:

1/2y – 2 = 1/3y

1/2y – 2 + 2 = 1/3y +2

1/2y = 1/3y + 2

Step 2b: Get the 1/3y to the left side of the equation by subtracting it from both sides.

1/2y = 1/3y + 2

1/2y – 1/3y = 1/3y + 2 – 1/3y

1/2y – 1/3y = 2

Step 2c: Combine 1/2y and 1/3y.

1/2y – 1/3y = 2

3/6y – 2/6y = 2

1/6y = 2

Step 2d: Multiply both sides by 6.

1/6y = 2

6/6y = 2*6

1y = 12

y = 12

Done.

Subtract 1/2y from both sides-

1/2y – 1/2y – 2 = 1/3y – 1/2y (1/2y – 1/2y cancels)

-2 = 1/3y – 1/2y (you have to get the least common denominator, which is 6. so multiply 1/3 * 2/2 and 1/2 * 3/3)

-2 = 2/6y – 3/6y (subtract)

-2 = -1/6y (then divide -2 by -1/6 to get y by itelf)

-2 / -1/6 = -1/6y / -1/6 (cancel the -1/6’s; and to divide by a fraction, you multiply by the reciprocal)

-2 * -6 = y

y = 12

Mulitply by 3y(2y – 2):

3y = 2y – 2

Subtract 2y from each side:

y = – 2.

Alternatively, if it really was

1/2y – 2 = 1/3y,

multiply by 6y:

3 – 12y = 2

Subtract 2:

1 – 12y = 0

Add 12y:

12y = 1

Divide by 12:

y = 1 / 12.

Some other people have taken the equation to be:

(1/2)y – 2 = (1/3)y.

They have correctly obtained y = 12.

The real solution depends on what the real question was.

First, you want to get rid of the fractions. In order to do that, you must find a common denominator, so it will get rid of ALL the fractions. Here, this is 6. So we multiply both sides by 6.

(6)(1/2y-2)=(6)(1/3y)

Using distributive property, we can simplify that. So next, we get:

3y-12=2y

Then we want to get y on one side. So we subtract 3y from both sides.

-12=-y

Now since the y is negative, we multiply both sides by -1 and we end up with:

12=y

See now, that wasn’t hard, was it? Keep practicing, you’ll get the hang of it!

Move your y’s to the left and the 2 to the left

1/2y – 1/3y = 2

Change all your bottoms to the same common #

3/6y – 2/6y = 2

Simplify on left side

1/6y = 2

Divide 2 by 1/6

y=12

* Place (12) in orginal question to check answer

3/2 – 6y = 1 (multiply both sides by 3y)

-6y = 1 – 3/2 (subtract 3/2 from both sides)

6y = 3/2 – 1 (multiply both sides by -1)

6y = 1/2

Think you can take it from here?

1/2y + 1/3y = 2

Find your lowest common denominator (LCD)

3/6y + 2/6y = 2

Combine like terms

5/6y = 2

Isolate unknown term

5 = 12y => 5/12 = y.

QED (Quite Easily Done)