$$ \begin{aligned} 3 \cdot \frac{x}{2}+7\frac{x}{5} &= 5&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot3 \cdot \frac{x}{2}+10\cdot7\frac{x}{5} &= 10\cdot5&& \text{cancel out the denominators} \\[1 em]15x+14x &= 50&& \text{simplify left side} \\[1 em]29x &= 50&& \text{ divide both sides by $ 29 $ } \\[1 em]x &= \frac{50}{29}&& \\[1 em] \end{aligned} $$

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