$$ \begin{aligned} 4a+5 &= 2+\frac{31}{4}a&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot4a+4\cdot5 &= 4\cdot2+4 \cdot \frac{31}{4}a&& \text{cancel out the denominators} \\[1 em]16a+20 &= 8+31a&& \text{move the $ \color{blue}{ 31a } $ to the left side and $ \color{blue}{ 20 }$ to the right} \\[1 em]16a-31a &= 8-20&& \text{simplify left and right hand side} \\[1 em]-15a &= -12&& \text{ divide both sides by $ -15 $ } \\[1 em]a &= \frac{-12}{-15}&& \\[1 em]a &= \frac{4}{5}&& \\[1 em] \end{aligned} $$

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