solve for y: y/5-2/5=1/3-y

Question

I am trying to help my student, but have been out of school since 1985. I don't remember how to do this problem.

Answer 1

Carlton's advice is a good way to get this problem started. I will start where he left off.

3y -6 = 5 -15y

We want the y's on one side of the equal sign and everything else on the other side. I will put the y's on the left. Add 15 y to both sides. (What you do to one side, you must do to the other.)

3y -6 +15y= 5 -15y+15y
18y -6=5
Adding 15y had the effect of moving all the y terms to the left side. Noe add 6 to both sides.
18y -6 +6 =5+6
18y=11
Now divide both sides by 18.
18y/18=11/18
Y=11/18 (Answer)

To check, write the original problem, but put 11/18 in for y. If the equation is true, then the answer is correct.

Y/5-2/5=1/3-y
(11/18)/5 -2/5=1/3-11/18
11/90-2/5=1/3-11/18
11/90-36/90=6/18-11/18
-25/90=-5/18
-5/18=-5/18 TRUE

Since the equation is true, our answer y=11/18 is correct.

Answer 2

There are a number of ways to solve this. Being that we have fractions in the equation, one method would be to eliminate the fractions. We do this by finding a Least Common Denominator (LCD), then multiplying each term by the LCD. In this case, it is 15.

So: 15(y/5) - 15(2/5) = 15(1/3) - 15(y)

This method will help us eliminate the fractions. Your new equation will be:

 

3y - 6 = 5 - 15y. Now combine like terms and solve for x.