$$ \begin{aligned} \frac{x}{3}+\frac{1}{2} &= 3x+\frac{1}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x}{3}+6\cdot\frac{1}{2} &= 6\cdot3x+6\cdot\frac{1}{6}&& \text{cancel out the denominators} \\[1 em]2x+3 &= 18x+1&& \text{move the $ \color{blue}{ 18x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]2x-18x &= 1-3&& \text{simplify left and right hand side} \\[1 em]-16x &= -2&& \text{ divide both sides by $ -16 $ } \\[1 em]x &= \frac{-2}{-16}&& \\[1 em]x &= \frac{1}{8}&& \\[1 em] \end{aligned} $$

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