$$ \begin{aligned} 3 &= \frac{6}{7}x+1&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7\cdot3 &= 7 \cdot \frac{6}{7}x+7\cdot1&& \text{cancel out the denominators} \\[1 em]21 &= 6x+7&& \text{ swap the left and right side of the equation } \\[1 em]6x+7 &= 21&& \text{ move 7 to the right } \\[1 em]6x &= 21-7&& \\[1 em]6x &= 14&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{14}{6}&& \\[1 em]x &= \frac{7}{3}&& \\[1 em] \end{aligned} $$

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