$$ \begin{aligned} 7-\frac{4}{5}x &= \frac{47}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot7-5 \cdot \frac{4}{5}x &= 5\cdot\frac{47}{5}&& \text{cancel out the denominators} \\[1 em]35-4x &= 47&& \text{ move 35 to the right } \\[1 em]-4x &= 47-35&& \\[1 em]-4x &= 12&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{12}{4}&& \\[1 em]x &= -3&& \\[1 em] \end{aligned} $$

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