[tex]\dfrac{1}{2}k-6=\dfrac{3}{7}k+4\\\\\text{We have the denominators: 2 and 7.}\\\\LCM(2,\ 7)=14\\\\\text{Multiply both sides of the equation by 14}.\\\\14\cdot\dfrac{1}{2}k-14\cdot6=14\cdot\dfrac{3}{7}k+14\cdot4\\\\7k-84=2\cdot3k+56\qquad\text{add 84 to both sides}\\\\7k=6k+140\qquad\text{subtract 6k from both sides}\\\\\boxed{k=140}[/tex]
