$$ \begin{aligned} \frac{1}{3}n+\frac{29}{6} &= 2(\frac{4}{3}n+\frac{2}{3})&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{1}{3}n+6\cdot\frac{29}{6} &= 6\cdot2(\frac{4}{3}n+\frac{2}{3})&& \text{cancel out the denominators} \\[1 em]2n+29 &= 6\cdot2(\frac{4}{3}n+\frac{2}{3})&& \text{simplify right side} \\[1 em]2n+29 &= 12(\frac{4}{3}n+\frac{2}{3})&& \\[1 em]2n+29 &= 12(\frac{4n}{3}+\frac{2}{3})&& \\[1 em]2n+29 &= 12 \cdot \frac{4n+2}{3}&& \\[1 em]2n+29 &= \frac{48n+24}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot2n+3\cdot29 &= 3 \cdot \frac{48n+24}{3}&& \text{cancel out the denominators} \\[1 em]6n+87 &= 48n+24&& \text{move the $ \color{blue}{ 48n } $ to the left side and $ \color{blue}{ 87 }$ to the right} \\[1 em]6n-48n &= 24-87&& \text{simplify left and right hand side} \\[1 em]-42n &= -63&& \text{ divide both sides by $ -42 $ } \\[1 em]n &= \frac{-63}{-42}&& \\[1 em]n &= \frac{3}{2}&& \\[1 em] \end{aligned} $$

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