$$ \begin{aligned} x-45-x+23-4 &= 0&& \text{simplify left side} \\[1 em]x-45-x+23-4 &= 0&& \\[1 em]-26 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ -26 = 0 } $ is FALSE, we conclude that the equation has no solution.
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