$$ \begin{aligned} \frac{x}{2}-\frac{5}{6}+3\frac{x}{4} &= 2&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{2}-12\cdot\frac{5}{6}+12\cdot3\frac{x}{4} &= 12\cdot2&& \text{cancel out the denominators} \\[1 em]6x-10+9x &= 24&& \text{simplify left side} \\[1 em]15x-10 &= 24&& \text{ move -10 to the right } \\[1 em]15x &= 24+10&& \\[1 em]15x &= 34&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{34}{15}&& \\[1 em] \end{aligned} $$

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