$$ \begin{aligned} \frac{x}{3}+7 &= 4x-5x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{x}{3}+3\cdot7 &= 3\cdot4x-3\cdot5x&& \text{cancel out the denominators} \\[1 em]x+21 &= 12x-15x&& \text{simplify right side} \\[1 em]x+21 &= -3x&& \text{move the $ \color{blue}{ -3x } $ to the left side and $ \color{blue}{ 21 }$ to the right} \\[1 em]x+3x &= -21&& \text{simplify left side} \\[1 em]4x &= -21&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{21}{4}&& \\[1 em] \end{aligned} $$

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