$$\frac{x+1}{5} = \frac{x-3}{9}$$

$$ \begin{aligned} \frac{x+1}{5} &= \frac{x-3}{9}&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45 \cdot \frac{x+1}{5} &= 45 \cdot \frac{x-3}{9}&& \text{cancel out the denominators} \\[1 em]9x+9 &= 5x-15&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]9x-5x &= -15-9&& \text{simplify left and right hand side} \\[1 em]4x &= -24&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{24}{4}&& \\[1 em]x &= -6&& \\[1 em] \end{aligned} $$

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