$$ \begin{aligned} 3x-\frac{9}{5}x-9 &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot3x-5 \cdot \frac{9}{5}x-5\cdot9 &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]15x-9x-45 &= 0&& \text{simplify left side} \\[1 em]6x-45 &= 0&& \text{ move the constants to the right } \\[1 em]6x &= 45&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{45}{6}&& \\[1 em]x &= \frac{15}{2}&& \\[1 em] \end{aligned} $$

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