$$ \begin{aligned} \frac{1}{3}(2x-5)+\frac{3}{4}(3x+1) &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{1}{3}(2x-5)+12\frac{3}{4}(3x+1) &= 12\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]8x-20+27x+9 &= 10&& \text{simplify left side} \\[1 em]35x-11 &= 10&& \text{ move -11 to the right } \\[1 em]35x &= 10+11&& \\[1 em]35x &= 21&& \text{ divide both sides by $ 35 $ } \\[1 em]x &= \frac{21}{35}&& \\[1 em]x &= \frac{3}{5}&& \\[1 em] \end{aligned} $$

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