$$ \begin{aligned} \frac{5x-3}{2} &= \frac{x+9}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{5x-3}{2} &= 2 \cdot \frac{x+9}{2}&& \text{cancel out the denominators} \\[1 em]5x-3 &= x+9&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]5x-x &= 9+3&& \text{simplify left and right hand side} \\[1 em]4x &= 12&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{12}{4}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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