$$x-\frac{8}{5} = x+\frac{7}{10}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x-\frac{8}{5} &= x+\frac{7}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x-10\cdot\frac{8}{5} &= 10x+10\cdot\frac{7}{10}&& \text{cancel out the denominators} \\[1 em]10x-16 &= 10x+7&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -16 }$ to the right} \\[1 em]10x-10x &= 7+16&& \text{simplify left and right hand side} \\[1 em]10x-10x &= 23&& \\[1 em]0 &= 23&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 23 } $ is FALSE, we conclude that the equation has no solution.
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