Question
$$x+\frac{1}{2}\cdot(100-x)\cdot2 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+\frac{1}{2}\cdot(100-x)\cdot2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2 \cdot \frac{1}{2}\cdot(100-x)\cdot2 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x-2x+200 &= 0&& \text{simplify left side} \\[1 em]200 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 200 = 0 } $ is FALSE, we conclude that the equation has no solution.
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