$$ \begin{aligned} \frac{1}{2}x+\frac{1}{3}x &= 5&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{1}{2}x+6\frac{1}{3}x &= 6\cdot5&& \text{cancel out the denominators} \\[1 em]3x+2x &= 30&& \text{simplify left side} \\[1 em]5x &= 30&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{30}{5}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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