$$ \begin{aligned} \frac{10}{x} &= \frac{5}{3}&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3\cdot\frac{10}{x} &= x\cdot3\cdot\frac{5}{3}&& \text{cancel out the denominators} \\[1 em]30 &= 5x&& \text{ swap the left and right side of the equation } \\[1 em]5x &= 30&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{30}{5}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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