$$ \begin{aligned} \frac{x}{2}+\frac{x}{6} &= 7&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x}{2}+6\frac{x}{6} &= 6\cdot7&& \text{cancel out the denominators} \\[1 em]3x+x &= 42&& \text{simplify left side} \\[1 em]4x &= 42&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{42}{4}&& \\[1 em]x &= \frac{21}{2}&& \\[1 em] \end{aligned} $$

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