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

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