$$ \begin{aligned} \frac{4}{2x+4} &= \frac{7}{5x+1}&& \text{multiply ALL terms by } \color{blue}{ (2x+4)(5x+1) }. \\[1 em](2x+4)(5x+1)\cdot\frac{4}{2x+4} &= (2x+4)(5x+1)\cdot\frac{7}{5x+1}&& \text{cancel out the denominators} \\[1 em]20x+4 &= 14x+28&& \text{move the $ \color{blue}{ 14x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]20x-14x &= 28-4&& \text{simplify left and right hand side} \\[1 em]6x &= 24&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{24}{6}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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