$$ \begin{aligned} \frac{1}{4}a+\frac{15}{4} &= \frac{5}{2}-a&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}a+4\cdot\frac{15}{4} &= 4\cdot\frac{5}{2}-4a&& \text{cancel out the denominators} \\[1 em]a+15 &= 10-4a&& \text{move the $ \color{blue}{ -4a } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]a+4a &= 10-15&& \text{simplify left and right hand side} \\[1 em]5a &= -5&& \text{ divide both sides by $ 5 $ } \\[1 em]a &= -\frac{5}{5}&& \\[1 em]a &= -1&& \\[1 em] \end{aligned} $$

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