$$ \begin{aligned} \frac{9}{2}+\frac{3}{2}k &= 18-3k&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot\frac{9}{2}+2\frac{3}{2}k &= 2\cdot18-2\cdot3k&& \text{cancel out the denominators} \\[1 em]9+3k &= 36-6k&& \text{move the $ \color{blue}{ -6k } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]3k+6k &= 36-9&& \text{simplify left and right hand side} \\[1 em]9k &= 27&& \text{ divide both sides by $ 9 $ } \\[1 em]k &= \frac{27}{9}&& \\[1 em]k &= 3&& \\[1 em] \end{aligned} $$

This page was created using