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