Answer:
[tex]\large\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]\dfrac{x-2}{3}+\dfrac{1}{6}=\dfrac{5}{6}\qquad\text{multiply both sides by 6}\\\\6\!\!\!\!\diagup^2\cdot\dfrac{x-2}{3\!\!\!\!\diagup_1}+6\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_1}=6\!\!\!\!\diagup^1\cdot\dfrac{5}{6\!\!\!\!\diagup_1}\\\\2(x-2)+1=5\qquad\text{use distributive property}\\\\(2)(x)+(2)(-2)+1=5\\\\2x-4+1=5\\\\2x-3=5\qquad\text{add 3 to both sides}\\\\2x-3+3=5+3\\\\2x=8\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{8}{2}\\\\x=4[/tex]
