$$ \begin{aligned} \frac{1}{2}x+\frac{2}{3} &= \frac{41}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{1}{2}x+6\cdot\frac{2}{3} &= 6\cdot\frac{41}{2}&& \text{cancel out the denominators} \\[1 em]3x+4 &= 123&& \text{ move 4 to the right } \\[1 em]3x &= 123-4&& \\[1 em]3x &= 119&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{119}{3}&& \\[1 em] \end{aligned} $$

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