$$x-7 = \frac{3x+13}{20}$$

$$ \begin{aligned} x-7 &= \frac{3x+13}{20}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20x-20\cdot7 &= 20 \cdot \frac{3x+13}{20}&& \text{cancel out the denominators} \\[1 em]20x-140 &= 3x+13&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -140 }$ to the right} \\[1 em]20x-3x &= 13+140&& \text{simplify left and right hand side} \\[1 em]17x &= 153&& \text{ divide both sides by $ 17 $ } \\[1 em]x &= \frac{153}{17}&& \\[1 em]x &= 9&& \\[1 em] \end{aligned} $$

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