Question

How do you solve `20/x=-5/2`?

Answer 1

`x = -8`

Explanation:

First, you need to multiply each side by a common denominator to eliminate the fractions and keep the equation balanced. In this case the common denominator is `2x`:

`((2x)*20)/x = -(2x*-5)/2`

`((2cancel(x))*20)/cancel(x) = -(cancel(2)x*5)/cancel(2)`

`2*20 = -5x`

`-5x = 40`

Now we can solve for `x` while keeping the equation balanced:

`(-5x)/-5 = 40/(-5)`

`(cancel(-5)x)/cancel(-5) = -8`

`x = -8`

Answer 2

`x=-8`

Explanation:

When we have a fraction equal to another fraction, we can solve using the method of `color(blue)"cross-multiplication"`

The negative sign on the right side must be attached to either the 5 or the 2 but NOT BOTH. as this would give a positive result. I'm attaching it to the 2.

`rArrcolor(blue)(20)/color(red)(x)=color(red)(5)/color(blue)(-2)`

To cross-multiply, multiply the terms in `color(red)"red"` and the terms in `color(blue)"blue"` and equate them.

`rArrcolor(red)(5x)=(color(blue)(20)xxcolor(blue)(-2))`

`rArr5x=-40`

To solve for x, divide both sides by 5

`(cancel(5) x)/cancel(5)=(-40)/5`

`rArrx=-8" is the solution"`