$$ \begin{aligned} \frac{3}{11}x+2 &= 5x-102&& \text{multiply ALL terms by } \color{blue}{ 11 }. \\[1 em]11 \cdot \frac{3}{11}x+11\cdot2 &= 11\cdot5x-11\cdot102&& \text{cancel out the denominators} \\[1 em]3x+22 &= 55x-1122&& \text{move the $ \color{blue}{ 55x } $ to the left side and $ \color{blue}{ 22 }$ to the right} \\[1 em]3x-55x &= -1122-22&& \text{simplify left and right hand side} \\[1 em]-52x &= -1144&& \text{ divide both sides by $ -52 $ } \\[1 em]x &= \frac{-1144}{-52}&& \\[1 em]x &= 22&& \\[1 em] \end{aligned} $$

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