$$ \begin{aligned} \frac{x-1}{2} &= \frac{x+9}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{x-1}{2} &= 4 \cdot \frac{x+9}{4}&& \text{cancel out the denominators} \\[1 em]2x-2 &= x+9&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]2x-x &= 9+2&& \text{simplify left and right hand side} \\[1 em]x &= 11&& \\[1 em]x &= 11&& \\[1 em] \end{aligned} $$

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