$$\frac{3}{2}x+\frac{1}{5} = \frac{9}{4}x$$

$$ \begin{aligned} \frac{3}{2}x+\frac{1}{5} &= \frac{9}{4}x&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{3}{2}x+20\cdot\frac{1}{5} &= 20 \cdot \frac{9}{4}x&& \text{cancel out the denominators} \\[1 em]30x+4 &= 45x&& \text{move the $ \color{blue}{ 45x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]30x-45x &= -4&& \text{simplify left side} \\[1 em]-15x &= -4&& \text{ divide both sides by $ -15 $ } \\[1 em]x &= \frac{-4}{-15}&& \\[1 em]x &= \frac{4}{15}&& \\[1 em] \end{aligned} $$

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