Question
$$\frac{x}{12}+1 = \frac{x}{3}-\frac{x}{4}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{x}{12}+1 &= \frac{x}{3}-\frac{x}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{12}+12\cdot1 &= 12 \cdot \frac{x}{3}-12\frac{x}{4}&& \text{cancel out the denominators} \\[1 em]x+12 &= 4x-3x&& \text{simplify right side} \\[1 em]x+12 &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]x-x &= -12&& \text{simplify left side} \\[1 em]x-x &= -12&& \\[1 em]0 &= -12&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -12 } $ is FALSE, we conclude that the equation has no solution.
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