$$ \begin{aligned} \frac{3x+21}{7} &= 8x-15&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{3x+21}{7} &= 7\cdot8x-7\cdot15&& \text{cancel out the denominators} \\[1 em]3x+21 &= 56x-105&& \text{move the $ \color{blue}{ 56x } $ to the left side and $ \color{blue}{ 21 }$ to the right} \\[1 em]3x-56x &= -105-21&& \text{simplify left and right hand side} \\[1 em]-53x &= -126&& \text{ divide both sides by $ -53 $ } \\[1 em]x &= \frac{-126}{-53}&& \\[1 em]x &= \frac{126}{53}&& \\[1 em] \end{aligned} $$

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