Question

How do you solve `2/9w-1/4=5/6`?

Answer 1

Sere the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(36)` to eliminate the fractions while keeping the equation balanced:

`color(red)(36)(2/9w - 1/4) = color(red)(36) xx 5/6`

`(color(red)(36) xx 2/9w) - (color(red)(36) xx 1/4) = cancel(color(red)(36))6 xx 5/color(red)(cancel(color(black)(6)))`

`(cancel(color(red)(36))4 xx 2/color(red)(cancel(color(black)(9)))w) - (cancel(color(red)(36))9 xx 1/color(red)cancel(color(black)(4)))) = 30`

`8w - 9 = 30`

Next, add `color(red)(9)` to each side of the equation to isolate the `w` term while keeping the equation balanced:

`8w - 9 + color(red)(9) = 30 + color(red)(9)`

`8w - 0 = 39`

`8w = 39`

Now, divide each side of the equation by `color(red)(8)` to solve for `w` while keeping the equation balanced:

`(8w)/color(red)(8) = 39/color(red)(8)`

`(color(red)(cancel(color(black)(8)))w)/cancel(color(red)(8)) = 39/8`

`w = 39/8`