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