$$ \begin{aligned} 2x+\frac{2}{22} &= 3&& \text{multiply ALL terms by } \color{blue}{ 22 }. \\[1 em]22\cdot2x+22\cdot\frac{2}{22} &= 22\cdot3&& \text{cancel out the denominators} \\[1 em]44x+2 &= 66&& \text{ move 2 to the right } \\[1 em]44x &= 66-2&& \\[1 em]44x &= 64&& \text{ divide both sides by $ 44 $ } \\[1 em]x &= \frac{64}{44}&& \\[1 em]x &= \frac{16}{11}&& \\[1 em] \end{aligned} $$

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