$$\frac{7}{2x-3} = \frac{4}{x}$$

$$ \begin{aligned} \frac{7}{2x-3} &= \frac{4}{x}&& \text{multiply ALL terms by } \color{blue}{ (2x-3)x }. \\[1 em](2x-3)x\cdot\frac{7}{2x-3} &= (2x-3)x\cdot\frac{4}{x}&& \text{cancel out the denominators} \\[1 em]7x &= 8x-12&& \text{move the $ \color{blue}{ 8x } $ to the left side} \\[1 em]7x-8x &= -12&& \text{simplify left side} \\[1 em]-x &= -12&& \text{switch signs on both sides} \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

This page was created using