$$\frac{x+2}{x+9} = \frac{4}{2}$$

$$ \begin{aligned} \frac{x+2}{x+9} &= \frac{4}{2}&& \text{multiply ALL terms by } \color{blue}{ (x+9)\cdot2 }. \\[1 em](x+9)\cdot2 \cdot \frac{x+2}{x+9} &= (x+9)\cdot2\cdot\frac{4}{2}&& \text{cancel out the denominators} \\[1 em]2x+4 &= 4x+36&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]2x-4x &= 36-4&& \text{simplify left and right hand side} \\[1 em]-2x &= 32&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{32}{2}&& \\[1 em]x &= -16&& \\[1 em] \end{aligned} $$

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