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

1 Answer
Apr 24, 2017

Answer:

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#