Algebra 2 Common Core

$x=\dfrac{3}{7}$
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 $x=\dfrac{3}{7}$.