$$ \begin{aligned} \frac{41}{3}x-\frac{1}{2} &= \frac{32}{5}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{41}{3}x-30\cdot\frac{1}{2} &= 30\cdot\frac{32}{5}&& \text{cancel out the denominators} \\[1 em]410x-15 &= 192&& \text{ move -15 to the right } \\[1 em]410x &= 192+15&& \\[1 em]410x &= 207&& \text{ divide both sides by $ 410 $ } \\[1 em]x &= \frac{207}{410}&& \\[1 em] \end{aligned} $$

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