$$ \begin{aligned} 5c+16+\frac{1}{2} &= 13+\frac{1}{2}+10c&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot5c+2\cdot16+2\cdot\frac{1}{2} &= 2\cdot13+2\cdot\frac{1}{2}+2\cdot10c&& \text{cancel out the denominators} \\[1 em]10c+32+1 &= 26+1+20c&& \text{simplify left and right hand side} \\[1 em]10c+33 &= 20c+27&& \text{move the $ \color{blue}{ 20c } $ to the left side and $ \color{blue}{ 33 }$ to the right} \\[1 em]10c-20c &= 27-33&& \text{simplify left and right hand side} \\[1 em]-10c &= -6&& \text{ divide both sides by $ -10 $ } \\[1 em]c &= \frac{-6}{-10}&& \\[1 em]c &= \frac{3}{5}&& \\[1 em] \end{aligned} $$

This page was created using