$$ \begin{aligned} x\cdot4+\frac{1}{2}x\cdot2-\frac{1}{2}x-\frac{1}{4} &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x\cdot4+4 \cdot \frac{1}{2}x\cdot2-4\frac{1}{2}x-4\cdot\frac{1}{4} &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]16x+4x-2x-1 &= 0&& \text{simplify left side} \\[1 em]18x-1 &= 0&& \text{ move the constants to the right } \\[1 em]18x &= 1&& \text{ divide both sides by $ 18 $ } \\[1 em]x &= \frac{1}{18}&& \\[1 em] \end{aligned} $$

This page was created using