Question

How do you solve `\frac { y } { 6} - \frac { 2y } { 5} = 1+ \frac { y } { 3}`?

Answer 1

`y=-30/17`

Explanation:

First, when you solve an algebraic equation with a fraction in it, you must always find the HCF (highest common factor) between them.

Therefore, in this case, the HCF between `6` (or also `3*2`), `5`, and `3` is `30` (in fact `3*2*5` since they are all prime numbers).

After that, you divide `30` by every denominator of the equation
and the number you get you multiply it by every numerator.

So

`y/6 * 5/5 - (2y)/5 * 6/6 = 1 * 30/30 + y/3 * 10/10`

`(5y)/5 - (2y)/5 = 30/30 + (10y)/10`

`(5y-12y)/30=(30+10y)/30`

Then you multiply both sides by `30`. In this way, you get rid of `30`, so now you have an equation without fractions.

`5y-12y=30+10y`

You move all the number with `y` on one side,

`5y-12y-10y=30`

You procede with the addictions,

`-17y=30`

And finally

`y=-30/17`

If there is anything you don't understand, please tell me.