Question

How do you solve `-4/(2-x)= -2`?

Answer 1

See the entire solution process below:

Explanation:

There are several ways to approach this. My first step is to multiply each side of the equation by `color(red)(1/-2)` to eliminate the negative signs and factor some of the numbers:

`color(red)(1/-2) * (-4)/(2 - x) = color(red)(1/-2) * -2`

`color(red)(1/color(black)(cancel(color(red)(-2)))) * (color(red)(cancel(color(black)(-4))) 2)/(2 - x) = color(red)(1/color(black)(cancel(color(red)(-2)))) * color(red)(cancel(color(black)(-2)))`

`2/(2 - x) = 1`

Next, multiply each side of the equation by `(color(red)(2 - x))` to eliminate the fraction while keeping the equation balanced:

`(color(red)(2 - x)) * 2/(2 - x) = 1(color(red)(2 - x))`

`cancel((color(red)(2 - x))) * 2/color(red)(cancel(color(black)(2 - x))) = 2 - x`

`2 = 2 - x`

Then subtract `color(red)(2)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(2) + 2 = -color(red)(2) + 2 - x`

`0 = 0 - x`

`0 = -x`

Now, multiply each side of the equation by `color(red)(-1)` to solve for `x` while keeping the equation balanced:

`color(red)(-1) * 0 = color(red)(-1) * -x`

`0 = x`

`x = 0`