$$ \begin{aligned} 4 \cdot \frac{x}{3} &= 7-x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot4 \cdot \frac{x}{3} &= 3\cdot7-3x&& \text{cancel out the denominators} \\[1 em]4x &= 21-3x&& \text{move the $ \color{blue}{ -3x } $ to the left side} \\[1 em]4x+3x &= 21&& \text{simplify left side} \\[1 em]7x &= 21&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{21}{7}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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