$$3 \cdot \frac{x}{2}+\frac{4}{7} = 9 \cdot \frac{x}{4}-\frac{13}{4}$$

$$ \begin{aligned} 3 \cdot \frac{x}{2}+\frac{4}{7} &= 9 \cdot \frac{x}{4}-\frac{13}{4}&& \text{multiply ALL terms by } \color{blue}{ 28 }. \\[1 em]28\cdot3 \cdot \frac{x}{2}+28\cdot\frac{4}{7} &= 28\cdot9 \cdot \frac{x}{4}-28\cdot\frac{13}{4}&& \text{cancel out the denominators} \\[1 em]42x+16 &= 63x-91&& \text{move the $ \color{blue}{ 63x } $ to the left side and $ \color{blue}{ 16 }$ to the right} \\[1 em]42x-63x &= -91-16&& \text{simplify left and right hand side} \\[1 em]-21x &= -107&& \text{ divide both sides by $ -21 $ } \\[1 em]x &= \frac{-107}{-21}&& \\[1 em]x &= \frac{107}{21}&& \\[1 em] \end{aligned} $$

This page was created using