Question
$$5+x-\frac{2}{3} = x+\frac{3}{8}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5+x-\frac{2}{3} &= x+\frac{3}{8}&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24\cdot5+24x-24\cdot\frac{2}{3} &= 24x+24\cdot\frac{3}{8}&& \text{cancel out the denominators} \\[1 em]120+24x-16 &= 24x+9&& \text{simplify left side} \\[1 em]24x+104 &= 24x+9&& \text{move the $ \color{blue}{ 24x } $ to the left side and $ \color{blue}{ 104 }$ to the right} \\[1 em]24x-24x &= 9-104&& \text{simplify left and right hand side} \\[1 em]24x-24x &= -95&& \\[1 em]0 &= -95&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -95 } $ is FALSE, we conclude that the equation has no solution.
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