$$x+\frac{1}{5} = x-\frac{3}{9}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+\frac{1}{5} &= x-\frac{3}{9}&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45x+45\cdot\frac{1}{5} &= 45x-45\cdot\frac{3}{9}&& \text{cancel out the denominators} \\[1 em]45x+9 &= 45x-15&& \text{move the $ \color{blue}{ 45x } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]45x-45x &= -15-9&& \text{simplify left and right hand side} \\[1 em]45x-45x &= -24&& \\[1 em]0 &= -24&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -24 } $ is FALSE, we conclude that the equation has no solution.
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