Step 1 :The given equation is \(\frac{x}{2}-\frac{5}{6}=\frac{1}{2}\)
Step 2 :First, add \(\frac{5}{6}\) to both sides of the equation to get rid of the -\(\frac{5}{6}\) on the left side. This gives us \(\frac{x}{2}=\frac{1}{2}+\frac{5}{6}\)
Step 3 :Simplify the right side of the equation to get \(\frac{x}{2}=\frac{4}{3}\)
Step 4 :Then, multiply both sides of the equation by 2 to solve for x. This gives us \(x=2*\frac{4}{3}\)
Step 5 :Simplify the right side of the equation to get \(x=\frac{8}{3}\)
Step 6 :Final Answer: The solution to the equation is \(\boxed{\frac{8}{3}}\)