$$\frac{5}{3}x+\frac{2}{3} = \frac{5}{1}+\frac{x}{2}$$

$$ \begin{aligned} \frac{5}{3}x+\frac{2}{3} &= \frac{5}{1}+\frac{x}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{5}{3}x+6\cdot\frac{2}{3} &= 6\cdot\frac{5}{1}+6\frac{x}{2}&& \text{cancel out the denominators} \\[1 em]10x+4 &= 30+3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]10x-3x &= 30-4&& \text{simplify left and right hand side} \\[1 em]7x &= 26&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{26}{7}&& \\[1 em] \end{aligned} $$

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