$$ \begin{aligned} 4x-\frac{1}{4}x &= 15&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot4x-4 \cdot \frac{1}{4}x &= 4\cdot15&& \text{cancel out the denominators} \\[1 em]16x-x &= 60&& \text{simplify left side} \\[1 em]15x &= 60&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{60}{15}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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