$$ \begin{aligned} \frac{x+3}{2}+2\frac{x}{7} &= 7&& \text{multiply ALL terms by } \color{blue}{ 14 }. \\[1 em]14 \cdot \frac{x+3}{2}+14\cdot2\frac{x}{7} &= 14\cdot7&& \text{cancel out the denominators} \\[1 em]7x+21+4x &= 98&& \text{simplify left side} \\[1 em]11x+21 &= 98&& \text{ move 21 to the right } \\[1 em]11x &= 98-21&& \\[1 em]11x &= 77&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{77}{11}&& \\[1 em]x &= 7&& \\[1 em] \end{aligned} $$

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