$$ \begin{aligned} 2(\frac{11}{2}-x) &= \frac{21}{3}+\frac{1}{15}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30\cdot2(\frac{11}{2}-x) &= 30\cdot\frac{21}{3}+30\cdot\frac{1}{15}&& \text{cancel out the denominators} \\[1 em]30\cdot2(\frac{11}{2}-x) &= 210+2&& \text{simplify left and right hand side} \\[1 em]60(\frac{11}{2}-x) &= 212&& \\[1 em]60 \cdot \frac{-2x+11}{2} &= 212&& \\[1 em]\frac{-120x+660}{2} &= 212&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{-120x+660}{2} &= 2\cdot212&& \text{cancel out the denominators} \\[1 em]-120x+660 &= 424&& \text{ move 660 to the right } \\[1 em]-120x &= 424-660&& \\[1 em]-120x &= -236&& \text{ divide both sides by $ -120 $ } \\[1 em]x &= \frac{-236}{-120}&& \\[1 em]x &= \frac{59}{30}&& \\[1 em] \end{aligned} $$

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