Answer
$x=\dfrac{3}{7}$
Work Step by Step
Using the properties of equality, the given equation, $
\dfrac{1}{2}-x=\dfrac{x}{6}
,$ is equivalent to
\begin{align*}\require{cancel}
6\left(\dfrac{1}{2}-x\right)&=\left(\dfrac{x}{6}\right)6
&\text{(multiply by the $LCD$)}
\\\\
3(1)-6(x)&=x(1)
\\
3-6x&=x
\\
-6x-x&=-3
\\
-7x&=-3
\\\\
\dfrac{-7x}{-7}&=\dfrac{-3}{-7}
\\\\
x&=\dfrac{3}{7}
.\end{align*}
Hence, the solution is $
x=\dfrac{3}{7}
$.
