$$ \begin{aligned} \frac{x}{2}-\frac{1}{5} &= \frac{x}{3}+\frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60 \cdot \frac{x}{2}-60\cdot\frac{1}{5} &= 60 \cdot \frac{x}{3}+60\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]30x-12 &= 20x+15&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]30x-20x &= 15+12&& \text{simplify left and right hand side} \\[1 em]10x &= 27&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{27}{10}&& \\[1 em] \end{aligned} $$

This page was created using