Question

How do you solve `5y - 10+ y + 40= 7y + 30- 4y`?

Answer 1

See the entire solution process below:

Explanation:

First, group and combine like terms on each side of the equation:

`5y - 10 + y + 40 = 7y + 30 - 4y`

`5y + y - 10 + 40 = 7y - 4y + 30`

`(5 + 1)y + 30 = (7 - 4)y + 30`

`6y + 30 = 3y + 30`

Next, subtract `color(red)(30)` and `color(blue)(3y)` from each side of the equation to isolate the `y` term while keeping the equation balanced:

`6y + 30 - color(red)(30) - color(blue)(3y) = 3y + 30 - color(red)(30) - color(blue)(3y)`

`6y - color(blue)(3y) + 30 - color(red)(30) = 3y - color(blue)(3y) + 30 - color(red)(30)`

`(6 - 3)y + 0 = 0 + 0`

`3y = 0`

Now, divide each side of the equation by `color(red)(3)` to solve for `y` while keeping the equation balanced:

`(3y)/color(red)(3) = 0/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 0`

`y = 0`