Question
$$(1+x)\cdot2-(x-1)\cdot2 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (1+x)\cdot2-(x-1)\cdot2 &= 0&& \text{simplify left side} \\[1 em]2+2x-(2x-2) &= 0&& \\[1 em]2+2x-2x+2 &= 0&& \\[1 em]2+2x-2x+2 &= 0&& \\[1 em]4 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 4 = 0 } $ is FALSE, we conclude that the equation has no solution.
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