$$ \begin{aligned} 3(x-\frac{9}{5}) &= 2x+1&& \text{simplify left side} \\[1 em]3 \cdot \frac{5x-9}{5} &= 2x+1&& \\[1 em]\frac{15x-27}{5} &= 2x+1&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{15x-27}{5} &= 5\cdot2x+5\cdot1&& \text{cancel out the denominators} \\[1 em]15x-27 &= 10x+5&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -27 }$ to the right} \\[1 em]15x-10x &= 5+27&& \text{simplify left and right hand side} \\[1 em]5x &= 32&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{32}{5}&& \\[1 em] \end{aligned} $$

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