$$ \begin{aligned} \frac{2}{3}(y-5) &= \frac{1}{6}(2y+2)&& \text{simplify left and right hand side} \\[1 em]\frac{2y-10}{3} &= \frac{2y+2}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{2y-10}{3} &= 6 \cdot \frac{2y+2}{6}&& \text{cancel out the denominators} \\[1 em]4y-20 &= 2y+2&& \text{move the $ \color{blue}{ 2y } $ to the left side and $ \color{blue}{ -20 }$ to the right} \\[1 em]4y-2y &= 2+20&& \text{simplify left and right hand side} \\[1 em]2y &= 22&& \text{ divide both sides by $ 2 $ } \\[1 em]y &= \frac{22}{2}&& \\[1 em]y &= 11&& \\[1 em] \end{aligned} $$

This page was created using