Question

How do you solve `7x+1/-8=x-3/4`?

Answer 1

See the entire solution process below:`x = -5/48`

Explanation:

First, multiply each side of the equation by `color(red)(8)` to eliminate the fractions to make working with the equation easier and keep the equation balanced:

`color(red)(8) xx (7x + 1/-8) = color(red)(8) xx (x - 3/4)`

`(color(red)(8) xx 7x) + (color(red)(8) xx 1/-8) = (color(red)(8) xx x) - (color(red)(8) xx 3/4)`

`56x + 8/-8 = 8x - 24/4`

`56x - 1 = 8x - 6`

Next, subtract `color(red)(8x)` and add `color(blue)(1)` to each side of the equation to isolate the `x` terms and keep the equation balanced:

`56x - 1 - color(red)(8x) + color(blue)(1) = 8x - 6 - color(red)(8x) + color(blue)(1)`

`56x - color(red)(8x) - 1 + color(blue)(1) = 8x - color(red)(8x) - 6 + color(blue)(1)`

`(56 - 8)x - 0 = 0 - 5`

`48x = -5`

Now, divide each side of the equation by `color(red)(48)` to solve for `x` while keeping the equation balanced:

`(48x)/color(red)(48) = -5/color(red)(48)`

`(color(red)(cancel(color(black)(48)))x)/cancel(color(red)(48)) = -5/48`

`x = -5/48`