Question
$$x-3 = 2 \cdot \frac{x^1}{2}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x-3 &= 2 \cdot \frac{x^1}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x-2\cdot3 &= 2\cdot2 \cdot \frac{x^1}{2}&& \text{cancel out the denominators} \\[1 em]2x-6 &= 2x&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]2x-2x &= 6&& \text{simplify left side} \\[1 em]2x-2x &= 6&& \\[1 em]0 &= 6&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 6 } $ is FALSE, we conclude that the equation has no solution.
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