$$x+\frac{2}{5} = x-2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+\frac{2}{5} &= x-2&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5x+5\cdot\frac{2}{5} &= 5x-5\cdot2&& \text{cancel out the denominators} \\[1 em]5x+2 &= 5x-10&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]5x-5x &= -10-2&& \text{simplify left and right hand side} \\[1 em]5x-5x &= -12&& \\[1 em]0 &= -12&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -12 } $ is FALSE, we conclude that the equation has no solution.
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