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:

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

$x = 2$
$x = -2/3$

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