Question

How do you solve `x-3/4=-9/10` by clearing the fractions?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(20)` (the LCD of both fractions) to eliminate the fractions while keeping the equation balanced:

`color(red)(20)(x - 3/4) = color(red)(20) xx -9/10`

`(color(red)(20) xx x) - (color(red)(20) xx 3/4) = cancel(color(red)(20))2 xx -9/color(red)(cancel(color(black)(10)))`

`20x - (cancel(color(red)(20))5 xx 3/color(red)(cancel(color(black)(4)))) = -18`

`20x - 15 = -18`

Next, add `color(red)(15)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`20x - 15 + color(red)(15) = -18 + color(red)(15)`

`20x - 0 = -3`

`20x = -3`

Now, divide each side of the equation by `color(red)(20)` to solve for `x` while keeping the equation balanced:

`(20x)/color(red)(20) = -3/color(red)(20)`

`(color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20)) = -3/20`

`x = -3/20`