$$ \begin{aligned} \frac{1}{21}x-\frac{4}{7} &= \frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ 21 }. \\[1 em]21 \cdot \frac{1}{21}x-21\cdot\frac{4}{7} &= 21\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]x-12 &= 14&& \text{ move -12 to the right } \\[1 em]x &= 14+12&& \\[1 em]x &= 26&& \\[1 em]x &= 26&& \\[1 em] \end{aligned} $$

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