$$ \begin{aligned} \frac{1}{10}d+\frac{1}{4}(d+8) &= \frac{41}{10}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{1}{10}d+20\frac{1}{4}(d+8) &= 20\cdot\frac{41}{10}&& \text{cancel out the denominators} \\[1 em]2d+5d+40 &= 82&& \text{simplify left side} \\[1 em]7d+40 &= 82&& \text{ move 40 to the right } \\[1 em]7d &= 82-40&& \\[1 em]7d &= 42&& \text{ divide both sides by $ 7 $ } \\[1 em]d &= \frac{42}{7}&& \\[1 em]d &= 6&& \\[1 em] \end{aligned} $$

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