$$\frac{5}{12}x-\frac{3}{4} = \frac{1}{2}x+\frac{5}{6}$$

$$ \begin{aligned} \frac{5}{12}x-\frac{3}{4} &= \frac{1}{2}x+\frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{5}{12}x-12\cdot\frac{3}{4} &= 12 \cdot \frac{1}{2}x+12\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]5x-9 &= 6x+10&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -9 }$ to the right} \\[1 em]5x-6x &= 10+9&& \text{simplify left and right hand side} \\[1 em]-x &= 19&& \text{switch signs on both sides} \\[1 em]x &= -19&& \\[1 em] \end{aligned} $$

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