How do you solve `10/5=(3v+10)/(v+4)`?

First, multiply each side of the equation by the common denominator of the two fractions `color(red)(5)color(blue)((v + 4))` to eliminate the fractions and keep the equation balanced:

`color(red)(5)color(blue)((v + 4)) xx 10/5 = color(red)(5)color(blue)((v + 4)) xx (3v + 10)/(v + 4)`

`cancel(color(red)(5))color(blue)((v + 4)) xx 10/color(red)(cancel(color(black)(5))) = color(red)(5)color(blue)(cancel((v + 4))) xx (3v + 10)/color(blue)(cancel(color(black)((v + 4))))`

`10(v + 4) = 5(3v + 10)`

Next, expand the terms in parenthesis:

`(10 xx v) + (10 xx 4) = (5 xx 3v) + (5 xx 10)`

`10v + 40 = 15v + 50`

Then, subtract `color(red)(10v)` and `color(blue)(50)` from each side of the equation to isolate the `v` term while keeping the equation balanced:

`10v - color(red)(10v) + 40 - color(blue)(50) = 15v - color(red)(10v) + 50 - color(blue)(50)`

`0 - 10 = 5v + 0`

`-10 = 5v`

Now, divide each side of the equation by `color(red)(5)` to solve for `v` while keeping the equation balanced:

`-10/color(red)(5) = (5v)/color(red)(5)`

`-2 = (color(red)(cancel(color(black)(5)))v)/cancel(color(red)(5))`

`-2 = v`

`v = -2`