$$ \begin{aligned} \frac{x-5}{3}+4x &= 7&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{x-5}{3}+3\cdot4x &= 3\cdot7&& \text{cancel out the denominators} \\[1 em]x-5+12x &= 21&& \text{simplify left side} \\[1 em]13x-5 &= 21&& \text{ move -5 to the right } \\[1 em]13x &= 21+5&& \\[1 em]13x &= 26&& \text{ divide both sides by $ 13 $ } \\[1 em]x &= \frac{26}{13}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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