$$ \begin{aligned} \frac{1}{4}p-\frac{1}{3} &= \frac{1}{2}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{1}{4}p-12\cdot\frac{1}{3} &= 12\cdot\frac{1}{2}&& \text{cancel out the denominators} \\[1 em]3p-4 &= 6&& \text{ move -4 to the right } \\[1 em]3p &= 6+4&& \\[1 em]3p &= 10&& \text{ divide both sides by $ 3 $ } \\[1 em]p &= \frac{10}{3}&& \\[1 em] \end{aligned} $$

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