$$ \begin{aligned} 2 \cdot \frac{x}{3}+\frac{x}{2} &= 7&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2 \cdot \frac{x}{3}+6\frac{x}{2} &= 6\cdot7&& \text{cancel out the denominators} \\[1 em]4x+3x &= 42&& \text{simplify left side} \\[1 em]7x &= 42&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{42}{7}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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