$$ \begin{aligned} 2+1-3x\cdot\frac{2}{7} &= 0&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7\cdot2+7\cdot1-73x\cdot\frac{2}{7} &= 7\cdot0&& \text{cancel out the denominators} \\[1 em]14+7-6x &= 0&& \text{simplify left side} \\[1 em]-6x+21 &= 0&& \text{ move the constants to the right } \\[1 em]-6x &= -21&& \text{ divide both sides by $ -6 $ } \\[1 em]x &= \frac{-21}{-6}&& \\[1 em]x &= \frac{7}{2}&& \\[1 em] \end{aligned} $$

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