$$ \begin{aligned} \frac{3}{2} &= 5d-\frac{1}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot\frac{3}{2} &= 2\cdot5d-2\cdot\frac{1}{2}&& \text{cancel out the denominators} \\[1 em]3 &= 10d-1&& \text{ swap the left and right side of the equation } \\[1 em]10d-1 &= 3&& \text{ move -1 to the right } \\[1 em]10d &= 3+1&& \\[1 em]10d &= 4&& \text{ divide both sides by $ 10 $ } \\[1 em]d &= \frac{4}{10}&& \\[1 em]d &= \frac{2}{5}&& \\[1 em] \end{aligned} $$

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