Question

How do you solve `6/9=8/x`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by the common denominator of the two fractions - `color(red)(9)color(blue)(x)`:

`color(red)(9)color(blue)(x) xx 6/9 = color(red)(9)color(blue)(x) xx 8/x`

`cancel(color(red)(9))color(blue)(x) xx 6/color(red)(cancel(color(black)(9))) = color(red)(9)cancel(color(blue)(x)) xx 8/color(blue)(cancel(color(black)(x)))`

`6x = 72`

Now, divide each side of the equation by `color(red)(6)` to solve for `x` while keeping the equation balanced:

`(6x)/color(red)(6) = 72/color(red)(6)`

`(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = 12`

`x = 12`