$$ \begin{aligned} \frac{2}{3}(6x-5) &= \frac{1}{2}(3x+4)&& \text{simplify left and right hand side} \\[1 em]\frac{12x-10}{3} &= \frac{3x+4}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{12x-10}{3} &= 6 \cdot \frac{3x+4}{2}&& \text{cancel out the denominators} \\[1 em]24x-20 &= 9x+12&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ -20 }$ to the right} \\[1 em]24x-9x &= 12+20&& \text{simplify left and right hand side} \\[1 em]15x &= 32&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{32}{15}&& \\[1 em] \end{aligned} $$

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