$$ \begin{aligned} 2x+\frac{2}{3} &= 8&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot2x+3\cdot\frac{2}{3} &= 3\cdot8&& \text{cancel out the denominators} \\[1 em]6x+2 &= 24&& \text{ move 2 to the right } \\[1 em]6x &= 24-2&& \\[1 em]6x &= 22&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{22}{6}&& \\[1 em]x &= \frac{11}{3}&& \\[1 em] \end{aligned} $$

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