Question

How do you solve `\frac { 5} { v - 4} = \frac { 4} { 2}`?

Answer 1

See a solution process below:

Explanation:

First, simplify the fraction on the right side of the equation:

`5/(v - 4) = (2 xx 2)/2`

`5/(v - 4) = (2 xx color(red)(cancel(color(black)(2))))/color(red)(cancel(color(black)(2)))`

`5/(v - 4) = 2`

Next, multiply each side of the equation by `color(red)((v - 4))` to eliminate the fraction while keeping the equation balanced:

`color(red)((v - 4)) xx 5/(v - 4) = 2color(red)((v - 4))`

`cancel(color(red)((v - 4))) xx 5/color(red)(cancel(color(black)(v - 4))) = (2 xx color(red)(v)) - (2 xx color(red)(4))`

`5 = 2v - 8`

Then, add `color(red)(8)` to each side of the equation to isolate the `v` term while keeping the equation balanced:

`5 + color(red)(8) = 2v - 8 + color(red)(8)`

`13 = 2v - 0`

`13 = 2v`

Now, divide each side of the equation by `color(red)(2)` to solve for `v` while keeping the equation balanced:

`13/color(red)(2) = (2v)/color(red)(2)`

`13/2 = (color(red)(cancel(color(black)(2)))v)/cancel(color(red)(2))`

`13/2 = v`

`v = 13/2`