$$ \begin{aligned} \frac{7}{x}-\frac{1}{2} &= \frac{3}{x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]x\cdot2\cdot\frac{7}{x}-x\cdot2\cdot\frac{1}{2} &= x\cdot2\cdot\frac{3}{x}&& \text{cancel out the denominators} \\[1 em]14-x &= 6&& \text{ move 14 to the right } \\[1 em]-x &= 6-14&& \\[1 em]-x &= -8&& \text{switch signs on both sides} \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

This page was created using