$$ \begin{aligned} \frac{3}{5}x+3 &= 12-x&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{3}{5}x+5\cdot3 &= 5\cdot12-5x&& \text{cancel out the denominators} \\[1 em]3x+15 &= 60-5x&& \text{move the $ \color{blue}{ -5x } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]3x+5x &= 60-15&& \text{simplify left and right hand side} \\[1 em]8x &= 45&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{45}{8}&& \\[1 em] \end{aligned} $$

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