$$ \begin{aligned} \frac{864}{1164}\cdot(2350-2006x)+2200x &= 2350&& \text{multiply ALL terms by } \color{blue}{ 1164 }. \\[1 em]1164 \cdot \frac{864}{1164}\cdot(2350-2006x)+1164\cdot2200x &= 1164\cdot2350&& \text{cancel out the denominators} \\[1 em]-1733184x+2030400+2560800x &= 2735400&& \text{simplify left side} \\[1 em]827616x+2030400 &= 2735400&& \text{ move 2030400 to the right } \\[1 em]827616x &= 2735400-2030400&& \\[1 em]827616x &= 705000&& \text{ divide both sides by $ 827616 $ } \\[1 em]x &= \frac{705000}{827616}&& \\[1 em]x &= \frac{29375}{34484}&& \\[1 em] \end{aligned} $$

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