$$ \begin{aligned} \frac{3}{5}-\frac{5}{6}x &= 2x+\frac{4}{3}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30\cdot\frac{3}{5}-30\frac{5}{6}x &= 30\cdot2x+30\cdot\frac{4}{3}&& \text{cancel out the denominators} \\[1 em]18-25x &= 60x+40&& \text{move the $ \color{blue}{ 60x } $ to the left side and $ \color{blue}{ 18 }$ to the right} \\[1 em]-25x-60x &= 40-18&& \text{simplify left and right hand side} \\[1 em]-85x &= 22&& \text{ divide both sides by $ -85 $ } \\[1 em]x &= -\frac{22}{85}&& \\[1 em] \end{aligned} $$

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