Question
$$-2x+4 = -2x+5$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} -2x+4 &= -2x+5&& \text{move the $ \color{blue}{ -2x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]-2x+2x &= 5-4&& \text{simplify left and right hand side} \\[1 em]-2x+2x &= 1&& \\[1 em]0 &= 1&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 1 } $ is FALSE, we conclude that the equation has no solution.
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