$$ \begin{aligned} \frac{1}{2}m-3 &= \frac{1}{4}m+3+3&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{2}m-4\cdot3 &= 4 \cdot \frac{1}{4}m+4\cdot3+4\cdot3&& \text{cancel out the denominators} \\[1 em]2m-12 &= m+12+12&& \text{simplify right side} \\[1 em]2m-12 &= m+24&& \text{move the $ \color{blue}{ m } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]2m-m &= 24+12&& \text{simplify left and right hand side} \\[1 em]m &= 36&& \\[1 em]m &= 36&& \\[1 em] \end{aligned} $$

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