Question

How do you solve `\frac { 8} { x } + \frac { 1} { 9} = \frac { 7} { x }`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(8/x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(8/x) + 8/x + 1/9 = -color(red)(8/x) + 7/x`

`0 + 1/9 = (-color(red)(8) + 7)/x`

`1/9 = -1/x`

Now, multiply each side of the equation by `color(red)(9)color(blue)(x)` to solve for `x` while keeping the equation balanced:

`color(red)(9)color(blue)(x) xx 1/9 = color(red)(9)color(blue)(x) xx -1/x`

`cancel(color(red)(9))color(blue)(x) xx 1/color(red)(cancel(color(black)(9))) = color(red)(9)cancel(color(blue)(x)) xx -1/color(blue)(cancel(color(black)(x)))`

`x = -9`