$$\frac{2}{3}x+\frac{1}{4} = \frac{11}{6}x-\frac{1}{3}$$

$$ \begin{aligned} \frac{2}{3}x+\frac{1}{4} &= \frac{11}{6}x-\frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{2}{3}x+12\cdot\frac{1}{4} &= 12 \cdot \frac{11}{6}x-12\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]8x+3 &= 22x-4&& \text{move the $ \color{blue}{ 22x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]8x-22x &= -4-3&& \text{simplify left and right hand side} \\[1 em]-14x &= -7&& \text{ divide both sides by $ -14 $ } \\[1 em]x &= \frac{-7}{-14}&& \\[1 em]x &= \frac{1}{2}&& \\[1 em] \end{aligned} $$

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