$$ \begin{aligned} 2 \cdot \frac{x}{3} &= \frac{x}{6}+1&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2 \cdot \frac{x}{3} &= 6 \cdot \frac{x}{6}+6\cdot1&& \text{cancel out the denominators} \\[1 em]4x &= x+6&& \text{move the $ \color{blue}{ x } $ to the left side} \\[1 em]4x-x &= 6&& \text{simplify left side} \\[1 em]3x &= 6&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{6}{3}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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