$$ \begin{aligned} 10x\cdot2+200+\frac{10}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]210x\cdot2+2\cdot200+2\cdot\frac{10}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]40x+400+10 &= 0&& \text{simplify left side} \\[1 em]40x+410 &= 0&& \text{ move the constants to the right } \\[1 em]40x &= -410&& \text{ divide both sides by $ 40 $ } \\[1 em]x &= -\frac{410}{40}&& \\[1 em]x &= -\frac{41}{4}&& \\[1 em] \end{aligned} $$

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