$$ \begin{aligned} 3 \cdot \frac{x}{5} &= 2x-7&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot3 \cdot \frac{x}{5} &= 5\cdot2x-5\cdot7&& \text{cancel out the denominators} \\[1 em]3x &= 10x-35&& \text{move the $ \color{blue}{ 10x } $ to the left side} \\[1 em]3x-10x &= -35&& \text{simplify left side} \\[1 em]-7x &= -35&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= \frac{-35}{-7}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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