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

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Answer 1 · 2017-05-31T13:56:58

#x = 2#
#x = -2/3#

First rearrange the equation so that it looks like this:

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

Make the right hand side of the equation have a denominator of 6.

#2/(3x) = (3x)/6 - 4/6#

= #2/(3x) = (3x-4)/6#

Now cross multiply to have a linear equation:

#3x(3x-4) = 12#

#9x^2 - 12x - 12 = 0#

The equation is divisible by 3 to give this equation:

#3x^2 - 4x - 4 = 0#

Now factorise the equation:

#(3x+2)(x-2) = 0#

#x = 2#
#x = -2/3#