$$ \begin{aligned} \frac{2}{3}+\frac{x}{3}+4 &= 2 \cdot \frac{x}{17}&& \text{multiply ALL terms by } \color{blue}{ 51 }. \\[1 em]51\cdot\frac{2}{3}+51\frac{x}{3}+51\cdot4 &= 51\cdot2 \cdot \frac{x}{17}&& \text{cancel out the denominators} \\[1 em]34+17x+204 &= 6x&& \text{simplify left side} \\[1 em]17x+238 &= 6x&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 238 }$ to the right} \\[1 em]17x-6x &= -238&& \text{simplify left side} \\[1 em]11x &= -238&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= -\frac{238}{11}&& \\[1 em] \end{aligned} $$

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