$$ \begin{aligned} 6(\frac{1}{3}y-1) &= \frac{1}{2}y\cdot6&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot6(\frac{1}{3}y-1) &= 6 \cdot \frac{1}{2}y\cdot6&& \text{cancel out the denominators} \\[1 em]6\cdot6(\frac{1}{3}y-1) &= 18y&& \text{simplify left side} \\[1 em]36(\frac{1}{3}y-1) &= 18y&& \\[1 em]36(\frac{y}{3}-1) &= 18y&& \\[1 em]36 \cdot \frac{y-3}{3} &= 18y&& \\[1 em]\frac{36y-108}{3} &= 18y&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{36y-108}{3} &= 3\cdot18y&& \text{cancel out the denominators} \\[1 em]36y-108 &= 54y&& \text{move the $ \color{blue}{ 54y } $ to the left side and $ \color{blue}{ -108 }$ to the right} \\[1 em]36y-54y &= 108&& \text{simplify left side} \\[1 em]-18y &= 108&& \text{ divide both sides by $ -18 $ } \\[1 em]y &= -\frac{108}{18}&& \\[1 em]y &= -6&& \\[1 em] \end{aligned} $$

This page was created using