Question
$$\frac{12}{11}+\frac{24}{11}+\frac{36}{11}+\frac{4}{11}+\frac{5}{11}+\frac{6}{11} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{12}{11}+\frac{24}{11}+\frac{36}{11}+\frac{4}{11}+\frac{5}{11}+\frac{6}{11} &= 0&& \text{multiply ALL terms by } \color{blue}{ 11 }. \\[1 em]11\cdot\frac{12}{11}+11\cdot\frac{24}{11}+11\cdot\frac{36}{11}+11\cdot\frac{4}{11}+11\cdot\frac{5}{11}+11\cdot\frac{6}{11} &= 11\cdot0&& \text{cancel out the denominators} \\[1 em]12+24+36+4+5+6 &= 0&& \text{simplify left side} \\[1 em]87 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 87 = 0 } $ is FALSE, we conclude that the equation has no solution.
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