$$ \begin{aligned} x+\frac{5}{2} &= 7&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2\cdot\frac{5}{2} &= 2\cdot7&& \text{cancel out the denominators} \\[1 em]2x+5 &= 14&& \text{ move 5 to the right } \\[1 em]2x &= 14-5&& \\[1 em]2x &= 9&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{9}{2}&& \\[1 em] \end{aligned} $$

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