How do you solve for x in #3/(2-x)=4#?

1 Answer
Mar 7, 2018

Answer:

#x = 5/4#

Explanation:

Starting from the equation:

#3/(2-x)=4#

We note that the #x# is in the denominator on the left hand side. We can do at least two things at this point, we can take the reciprocal of both sides or multiply both sides by a factor of #(2-x)#. Let's do the multiplication:

#(2-x)*3/(2-x)=(2-x)*4#

we can cancel the common factor of #(2-x)# on the left, and we can distribute the factor of #4# across the terms of #(2-x)# on the right to get

#cancel\color(red)((2-x))*3/cancel\color(red)((2-x)) = (\color(blue)4 *2-\color(blue)4 *x)#

#3 = 8-4x#

Next we need to get the x alone on one side. Lets subtract #8# from both sides:

#3-8 = 8-8-4x#

#-5 = -4x#

Then we can divide both sides by #-4#

#(-5)/(-4) = (-4)/(-4)x#

#5/4 = x#

which can be rewritten as

#x = 5/4#