$$ \begin{aligned} (2+\frac{1}{2})(4k+2) &= 12k&& \text{simplify left side} \\[1 em]\frac{5}{2}(4k+2) &= 12k&& \\[1 em]\frac{20k+10}{2} &= 12k&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{20k+10}{2} &= 2\cdot12k&& \text{cancel out the denominators} \\[1 em]20k+10 &= 24k&& \text{move the $ \color{blue}{ 24k } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]20k-24k &= -10&& \text{simplify left side} \\[1 em]-4k &= -10&& \text{ divide both sides by $ -4 $ } \\[1 em]k &= \frac{-10}{-4}&& \\[1 em]k &= \frac{5}{2}&& \\[1 em] \end{aligned} $$

This page was created using