Question

How do you solve `5/8x=-2/3` by clearing the fractions?

Answer 1

First, we need to multiply each side of the equation by the common denominator of the two fractions. The common denominator is `8 xx 3 = color(red)(24)`

`5/8x xx color(red)(24) = -2/3 xx color(red)(24)`

`5/8x xx (color(red)(3 xx 8)) = -2/3 xx (color(red)(3 xx 8))`

`5/color(red)(cancel(color(black)(8)))x xx (color(red)(3 xx cancel(8))) = -2/color(red)(cancel(color(black)(3))) xx (color(red)(cancel(3) xx 8))`

`5x xx 3 = -2 xx 8`

`15x = -16`

Now, we divide each side of the equation by `color(red)(15)` to solve for `x`:

`(15x)/color(red)(15) = -16/color(red)(15)`

`(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = -16/15`

`x = -16/15`