$$ \begin{aligned} \frac{3}{5}x+\frac{2}{5}x &= 19&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{3}{5}x+5\frac{2}{5}x &= 5\cdot19&& \text{cancel out the denominators} \\[1 em]3x+2x &= 95&& \text{simplify left side} \\[1 em]5x &= 95&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{95}{5}&& \\[1 em]x &= 19&& \\[1 em] \end{aligned} $$

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