Question
$$n+\frac{9}{8} = n+\frac{6}{2}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} n+\frac{9}{8} &= n+\frac{6}{2}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8n+8\cdot\frac{9}{8} &= 8n+8\cdot\frac{6}{2}&& \text{cancel out the denominators} \\[1 em]8n+9 &= 8n+24&& \text{move the $ \color{blue}{ 8n } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]8n-8n &= 24-9&& \text{simplify left and right hand side} \\[1 em]8n-8n &= 15&& \\[1 em]0 &= 15&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 15 } $ is FALSE, we conclude that the equation has no solution.
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