[tex]\dfrac{7}{12}x-\dfrac{1}{3}=\dfrac{1}{2}+\dfrac{3}{8}\\\\LCM(12,\ 3,\ 2,\ 8)=24\\\\\text{multiply both sides by 24}\\\\24\cdot\dfrac{7}{12}x-12\cdot\dfrac{1}{3}=12\cdot\dfrac{1}{2}+24\cdot\dfrac{3}{8}\\\\2\cdot7x-8=12+3\cdot3\\\\14x-8=12+9\\\\14x-8=21\qquad|\text{add 8 to both sides}\\\\14x=29\qquad|\text{divide both sides by 14}\\\\x=\dfrac{29}{14}[/tex]
