Answer
\[x=2\]
Work Step by Step
Consider the equation
\[\frac{2x}{3}=\frac{x}{6}+\frac{1}{1}\]
The least common denominator is 6 so multiply both the sides by 6 as follows:
\[\begin{align}
& \frac{2x}{3}\times 6=\left( \frac{x}{6}+\frac{1}{1} \right)\times 6 \\
& 4x=x+6
\end{align}\]
Simplifying
\[\begin{align}
& 3x=6 \\
& x=2
\end{align}\]
Now, to check it, put \[x=2\]in the equation
\[\begin{align}
& \frac{2x}{3}=\frac{x}{6}+1 \\
& \frac{2\times 2}{3}=\frac{2}{6}+1 \\
& \frac{4}{3}=\frac{1}{3}+1 \\
& \frac{4}{3}=\frac{4}{3}
\end{align}\]
which is true.
Hence, the solution of the given equation is\[x=2\].
