$$ \begin{aligned} \frac{1}{12}x+\frac{1}{15}(x-4) &= 1&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60 \cdot \frac{1}{12}x+60\frac{1}{15}(x-4) &= 60\cdot1&& \text{cancel out the denominators} \\[1 em]5x+4x-16 &= 60&& \text{simplify left side} \\[1 em]9x-16 &= 60&& \text{ move -16 to the right } \\[1 em]9x &= 60+16&& \\[1 em]9x &= 76&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{76}{9}&& \\[1 em] \end{aligned} $$

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