Question

How do you solve for y in `(y+5)/ 2 - y/3 =1`?

Answer 1

`y=-9`

Explanation:

Solve:

`(y+5)/2-y/3=1`

The LCM of `2` and `3` is `6`. Multiply both sides by `6`.

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

Simplify.

`(color(red)cancel(color(black)(6))^3(y+5))/color(red)cancel(color(black)(2))^1-(color(red)cancel(color(black)(6))^2(y))/color(red)cancel(color(black)(3))^1=1(6)`

`3(y+5)-2y=6`

Expand.

`3y+15-2y=6`

Subtract `15` from both sides.

`3y-2y=6-15`

Simplify.

`y=-9`

Answer 2

`y=-9`

Explanation:

As we know, when subtracting any fraction, we must have like denominators. To achieve this, let's multiply the first one by `3/3` and the second by `2/2`. We now have

`color(blue)((3/3))(y+5)/2-color(blue)((2/2))(y/3)=1`

Which simplifies to

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

Distributing the `3`, we now have

`(3y+15-2y)/6=1`

Combining like terms in the numerator, we get

`(y+15)/6=1`

Multiply both sides by `6` to get

`y+15=6`

Lastly, subtracting `15` from both sides gives us

`y=-9`

Hope this helps!