$$ \begin{aligned} \frac{7}{3}x+\frac{1}{3}x &= 8+\frac{5}{3}x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{7}{3}x+3\frac{1}{3}x &= 3\cdot8+3 \cdot \frac{5}{3}x&& \text{cancel out the denominators} \\[1 em]7x+x &= 24+5x&& \text{simplify left and right hand side} \\[1 em]8x &= 5x+24&& \text{move the $ \color{blue}{ 5x } $ to the left side} \\[1 em]8x-5x &= 24&& \text{simplify left side} \\[1 em]3x &= 24&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{24}{3}&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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