$$ \begin{aligned} 28(\frac{1}{4}y-8) &= \frac{1}{7}y\cdot28&& \text{multiply ALL terms by } \color{blue}{ 28 }. \\[1 em]28\cdot28(\frac{1}{4}y-8) &= 28 \cdot \frac{1}{7}y\cdot28&& \text{cancel out the denominators} \\[1 em]28\cdot28(\frac{1}{4}y-8) &= 112y&& \text{simplify left side} \\[1 em]784(\frac{1}{4}y-8) &= 112y&& \\[1 em]784(\frac{y}{4}-8) &= 112y&& \\[1 em]784 \cdot \frac{y-32}{4} &= 112y&& \\[1 em]\frac{784y-25088}{4} &= 112y&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{784y-25088}{4} &= 4\cdot112y&& \text{cancel out the denominators} \\[1 em]784y-25088 &= 448y&& \text{move the $ \color{blue}{ 448y } $ to the left side and $ \color{blue}{ -25088 }$ to the right} \\[1 em]784y-448y &= 25088&& \text{simplify left side} \\[1 em]336y &= 25088&& \text{ divide both sides by $ 336 $ } \\[1 em]y &= \frac{25088}{336}&& \\[1 em]y &= \frac{224}{3}&& \\[1 em] \end{aligned} $$

This page was created using