$$ \begin{aligned} 3 \cdot \frac{x}{5} &= 2 \cdot \frac{x}{3}+1&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15\cdot3 \cdot \frac{x}{5} &= 15\cdot2 \cdot \frac{x}{3}+15\cdot1&& \text{cancel out the denominators} \\[1 em]9x &= 10x+15&& \text{move the $ \color{blue}{ 10x } $ to the left side} \\[1 em]9x-10x &= 15&& \text{simplify left side} \\[1 em]-x &= 15&& \text{switch signs on both sides} \\[1 em]x &= -15&& \\[1 em] \end{aligned} $$

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