$$ \begin{aligned} \frac{7}{2} &= w-\frac{5}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot\frac{7}{2} &= 2w-2\cdot\frac{5}{2}&& \text{cancel out the denominators} \\[1 em]7 &= 2w-5&& \text{ swap the left and right side of the equation } \\[1 em]2w-5 &= 7&& \text{ move -5 to the right } \\[1 em]2w &= 7+5&& \\[1 em]2w &= 12&& \text{ divide both sides by $ 2 $ } \\[1 em]w &= \frac{12}{2}&& \\[1 em]w &= 6&& \\[1 em] \end{aligned} $$

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