$$ \begin{aligned} \frac{140}{127}\cdot\frac{107}{x} &= \frac{6}{5}&& \text{multiply ALL terms by } \color{blue}{ 127x\cdot5 }. \\[1 em]127x\cdot5 \cdot \frac{140}{127}\cdot\frac{107}{x} &= 127x\cdot5\cdot\frac{6}{5}&& \text{cancel out the denominators} \\[1 em]74900 &= 762x&& \text{ swap the left and right side of the equation } \\[1 em]762x &= 74900&& \text{ divide both sides by $ 762 $ } \\[1 em]x &= \frac{74900}{762}&& \\[1 em]x &= \frac{37450}{381}&& \\[1 em] \end{aligned} $$

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