$$ \begin{aligned} x &= x+7&& \text{move the $ \color{blue}{ x } $ to the left side} \\[1 em]x-x &= 7&& \text{simplify left side} \\[1 em]x-x &= 7&& \\[1 em]0 &= 7&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 7 } $ is FALSE, we conclude that the equation has no solution.
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