$$ \begin{aligned} 1-3 \cdot \frac{x}{3} &= x+\frac{2}{14}&& \text{multiply ALL terms by } \color{blue}{ 42 }. \\[1 em]42\cdot1-42\cdot3 \cdot \frac{x}{3} &= 42x+42\cdot\frac{2}{14}&& \text{cancel out the denominators} \\[1 em]42-42x &= 42x+6&& \text{move the $ \color{blue}{ 42x } $ to the left side and $ \color{blue}{ 42 }$ to the right} \\[1 em]-42x-42x &= 6-42&& \text{simplify left and right hand side} \\[1 em]-84x &= -36&& \text{ divide both sides by $ -84 $ } \\[1 em]x &= \frac{-36}{-84}&& \\[1 em]x &= \frac{3}{7}&& \\[1 em] \end{aligned} $$

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