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

Question

Eva Adamson · Accepted Answer

See the entire solution process below:

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#

Julia Adams · Answer

undefined To solve the equation -4/(2-x) = -2, you can follow these steps:

1. Multiply both sides of the equation by (2-x) to eliminate the denominator:
   -4 = -2(2-x)

2. Distribute -2 to both terms inside the parentheses:
   -4 = -4 + 2x

3. Simplify the equation by combining like terms:
   -4 = 2x - 4

4. Add 4 to both sides of the equation:
   0 = 2x

5. Divide both sides of the equation by 2:
   0/2 = 2x/2

6. Simplify the equation:
   0 = x

Therefore, the solution to the equation -4/(2-x) = -2 is x = 0.