$$ \begin{aligned} \frac{1}{2}(p+7)\cdot12 &= 150&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}(p+7)\cdot12 &= 2\cdot150&& \text{cancel out the denominators} \\[1 em]12p+84 &= 300&& \text{ move 84 to the right } \\[1 em]12p &= 300-84&& \\[1 em]12p &= 216&& \text{ divide both sides by $ 12 $ } \\[1 em]p &= \frac{216}{12}&& \\[1 em]p &= 18&& \\[1 em] \end{aligned} $$

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