$$ \begin{aligned} \frac{4}{5}x+\frac{1}{2} &= \frac{3}{5}x+\frac{3}{2}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{4}{5}x+10\cdot\frac{1}{2} &= 10 \cdot \frac{3}{5}x+10\cdot\frac{3}{2}&& \text{cancel out the denominators} \\[1 em]8x+5 &= 6x+15&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]8x-6x &= 15-5&& \text{simplify left and right hand side} \\[1 em]2x &= 10&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{10}{2}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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