$$ \begin{aligned} \frac{1}{2}(7d+4) &= 7-\frac{3}{2}d&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}(7d+4) &= 2\cdot7-2 \cdot \frac{3}{2}d&& \text{cancel out the denominators} \\[1 em]7d+4 &= 14-3d&& \text{move the $ \color{blue}{ -3d } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]7d+3d &= 14-4&& \text{simplify left and right hand side} \\[1 em]10d &= 10&& \text{ divide both sides by $ 10 $ } \\[1 em]d &= \frac{10}{10}&& \\[1 em]d &= 1&& \\[1 em] \end{aligned} $$

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