Question

If `w/x=y/z`, then what is the value of `x`?

Answer 1

First, multiply each side of the equation by `color(red)(x)color(blue)(z)` to eliminate the fractions while keeping the equation balanced:

`color(red)(x)color(blue)(z) xx w/x = color(red)(x)color(blue)(z) xx y/z`

`cancel(color(red)(x))color(blue)(z) xx w/color(red)(cancel(color(black)(x))) = color(red)(x)cancel(color(blue)(z)) xx y/color(blue)(cancel(color(black)(z)))`

`wz = xy`

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

`(wz)/color(red)(y) = (xy)/color(red)(y)`

`(wz)/y = (xcolor(red)(cancel(color(black)(y))))/cancel(color(red)(y))`

`(wz)/y = x`

`x = (wz)/y` When, `x != 0`, `z != 0`, `y != 0` and `(wz)/y != 0`