$$x+\frac{4}{5} = x-\frac{2}{4}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+\frac{4}{5} &= x-\frac{2}{4}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20x+20\cdot\frac{4}{5} &= 20x-20\cdot\frac{2}{4}&& \text{cancel out the denominators} \\[1 em]20x+16 &= 20x-10&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ 16 }$ to the right} \\[1 em]20x-20x &= -10-16&& \text{simplify left and right hand side} \\[1 em]20x-20x &= -26&& \\[1 em]0 &= -26&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -26 } $ is FALSE, we conclude that the equation has no solution.
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