$$ \begin{aligned} \frac{1}{7} &= \frac{x}{6}&& \text{multiply ALL terms by } \color{blue}{ 42 }. \\[1 em]42\cdot\frac{1}{7} &= 42 \cdot \frac{x}{6}&& \text{cancel out the denominators} \\[1 em]6 &= 7x&& \text{ swap the left and right side of the equation } \\[1 em]7x &= 6&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{6}{7}&& \\[1 em] \end{aligned} $$

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