$$ \begin{aligned} \frac{x}{7} &= \frac{x}{4}+1&& \text{multiply ALL terms by } \color{blue}{ 28 }. \\[1 em]28 \cdot \frac{x}{7} &= 28 \cdot \frac{x}{4}+28\cdot1&& \text{cancel out the denominators} \\[1 em]4x &= 7x+28&& \text{move the $ \color{blue}{ 7x } $ to the left side} \\[1 em]4x-7x &= 28&& \text{simplify left side} \\[1 em]-3x &= 28&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= -\frac{28}{3}&& \\[1 em] \end{aligned} $$

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