Question

How do you solve `(x+2)/(y-4)=3/4` for `y`?

Answer 1

See a solution process below:

Explanation:

First, because both sides of the equation are pure fractions we can flip the fractions and write the equation as:

`(y - 4)/(x + 2) = 4/3`

Next, multiply each side of the equation by `color(red)((x + 2))` to eliminate the fraction on the left side of the equation while keeping the equation balanced:

`color(red)((x + 2)) xx (y - 4)/(x + 2) = 4/3color(red)((x + 2))`

`cancel(color(red)((x + 2))) xx (y - 4)/color(red)(cancel(color(black)(x + 2))) = (4/3 xx color(red)(x)) + (4/3 xx color(red)(2))`

`y - 4 = 4/3x + 8/3`

Now, add `color(red)(4)` to each side of the equation to solve for `y` while keeping the equation balanced:

`y - 4 + color(red)(4) = 4/3x + 8/3 + color(red)(4)`

`y - 0 = 4/3x + 8/3 + (3/3 xx color(red)(4))`

`y = 4/3x + 8/3 + 12/3`

`y = 4/3x + 20/3`

Or

`y = 4/3(x + 5)`