Question

How do you solve for y in `3+6x = 11-4y`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(11)` from each side of the equation to isolate the `y` term while keeping the equation balanced:

`-color(red)(11) + 3 + 6x = -color(red)(11) + 11 - 4y`

`-8 + 6x = 0 - 4y`

`-8 + 6x = -4y`

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

`(-8 + 6x)/color(red)(-4) = (-4y)/color(red)(-4)`

`(-8)/color(red)(-4) + (6x)/color(red)(-4) = (color(red)(cancel(color(Black)(-4)))y)/cancel(color(red)(-4))`

`2 - 6/4x = y`

`2 - (2 xx 3)/(2 xx 2)x = y`

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

`2 - 3/2/x = y`

`y = 2 - 3/2x`

Or

`y = -3/2x + 2`