Question

How do you solve `8/9=(w-2)/6`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side by a common denominator for the fractions, in this case `color(red)(18)`, to eliminate the fractions while keeping the equation balanced:

`color(red)(18) xx 8/9 = color(red)(18) xx (w - 2)/6`

`cancel(color(red)(18)) 2 xx 8/color(red)(cancel(color(black)(9))) = cancel(color(red)(18)) 3 xx (w - 2)/color(red)(cancel(color(black)(6)))`

`16 = 3(w - 2)`

`16 = (3 xx w) - (3 xx 2)`

`16 = 3w - 6`

Next, add `color(red)(6)` to each side of the equation to isolate the `w` term while keeping the equation balanced:

`16 + color(red)(6) = 3w - 6 + color(red)(6)`

`22 = 3w - 0`

`22 = 3w`

Now, divide each side of the equation by `color(red)(3)` to solve for `w` while keeping the equation balanced:

`22/color(red)(3) = (3w)/color(red)(3)`

`22/3 = (color(red)(cancel(color(black)(3)))w)/cancel(color(red)(3))`

`22/3 = w`

`w = 22/3`