Question

How do you solve `8/6=(k-4)/(k-3)`?

Answer 1

See the entire solution process below:

Explanation:

Multiply each side of the equation by `color(red)(6)(color(blue)(k - 3))` to eliminate the fractions while keeping the equation balanced:

`color(red)(6)(color(blue)(k - 3)) xx 8/6 = color(red)(6)(color(blue)(k - 3)) xx (k - 4)/(k - 3)`

`cancel(color(red)(6))(color(blue)(k - 3)) xx 8/color(red)(cancel(color(black)(6))) = color(red)(6)cancel((color(blue)(k - 3))) xx (k - 4)/color(blue)(cancel(color(black)(k - 3)))`

`8(color(blue)(k - 3)) = color(red)(6)(k - 4)`

Next, expand the terms within parenthesis on each side of the equation:

`(8 xx color(blue)(k)) - (8 xx color(blue)(3)) = (color(red)(6) xx k) - (color(red)(6) xx 4)`

`8k - 24 = 6k - 24`

Then, add `color(red)(24)` and subtract `color(blue)(6k)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`8k - 24 + color(red)(24) - color(blue)(6k) = 6k - 24 + color(red)(24) - color(blue)(6k)`

`8k - color(blue)(6k) - 24 + color(red)(24) = 6k - color(blue)(6k) - 24 + color(red)(24)`

`2k - 0 = 0 - 0`

`2k = 0`

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

`(2k)/color(red)(2) = 0/color(red)(2)`

`(color(red)(cancel(color(black)(2)))k)/cancel(color(red)(2)) = 0`

`k = 0`