$$ \begin{aligned} \frac{x\cdot4+1}{x\cdot3+x} &= \frac{7}{2}&& \text{multiply ALL terms by } \color{blue}{ (x\cdot3+x)\cdot2 }. \\[1 em](x\cdot3+x)\cdot2 \cdot \frac{x\cdot4+1}{x\cdot3+x} &= (x\cdot3+x)\cdot2\cdot\frac{7}{2}&& \text{cancel out the denominators} \\[1 em]8x+2 &= 28x&& \text{move the $ \color{blue}{ 28x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]8x-28x &= -2&& \text{simplify left side} \\[1 em]-20x &= -2&& \text{ divide both sides by $ -20 $ } \\[1 em]x &= \frac{-2}{-20}&& \\[1 em]x &= \frac{1}{10}&& \\[1 em] \end{aligned} $$

This page was created using