$$\frac{x+2}{5} = \frac{x-2}{3}$$

$$ \begin{aligned} \frac{x+2}{5} &= \frac{x-2}{3}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{x+2}{5} &= 15 \cdot \frac{x-2}{3}&& \text{cancel out the denominators} \\[1 em]3x+6 &= 5x-10&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]3x-5x &= -10-6&& \text{simplify left and right hand side} \\[1 em]-2x &= -16&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-16}{-2}&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

This page was created using