$$x-\frac{3}{2} = x+\frac{1}{3}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x-\frac{3}{2} &= x+\frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6x-6\cdot\frac{3}{2} &= 6x+6\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]6x-9 &= 6x+2&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -9 }$ to the right} \\[1 em]6x-6x &= 2+9&& \text{simplify left and right hand side} \\[1 em]6x-6x &= 11&& \\[1 em]0 &= 11&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 11 } $ is FALSE, we conclude that the equation has no solution.
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