$$ \begin{aligned} \frac{3x+4}{5} &= \frac{x-2}{6}+\frac{5x+2}{4}&& \text{multiply ALL terms by } \color{blue}{ 60 }. \\[1 em]60 \cdot \frac{3x+4}{5} &= 60 \cdot \frac{x-2}{6}+60\frac{5x+2}{4}&& \text{cancel out the denominators} \\[1 em]36x+48 &= 10x-20+75x+30&& \text{simplify right side} \\[1 em]36x+48 &= 85x+10&& \text{move the $ \color{blue}{ 85x } $ to the left side and $ \color{blue}{ 48 }$ to the right} \\[1 em]36x-85x &= 10-48&& \text{simplify left and right hand side} \\[1 em]-49x &= -38&& \text{ divide both sides by $ -49 $ } \\[1 em]x &= \frac{-38}{-49}&& \\[1 em]x &= \frac{38}{49}&& \\[1 em] \end{aligned} $$

This page was created using