$$ \begin{aligned} \frac{3}{4}x+\frac{1}{4} &= \frac{2}{3}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{3}{4}x+12\cdot\frac{1}{4} &= 12\cdot\frac{2}{3}&& \text{cancel out the denominators} \\[1 em]9x+3 &= 8&& \text{ move 3 to the right } \\[1 em]9x &= 8-3&& \\[1 em]9x &= 5&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{5}{9}&& \\[1 em] \end{aligned} $$

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