Question
$$4x+\frac{12}{5} = 4x-12$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4x+\frac{12}{5} &= 4x-12&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot4x+5\cdot\frac{12}{5} &= 5\cdot4x-5\cdot12&& \text{cancel out the denominators} \\[1 em]20x+12 &= 20x-60&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]20x-20x &= -60-12&& \text{simplify left and right hand side} \\[1 em]20x-20x &= -72&& \\[1 em]0 &= -72&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -72 } $ is FALSE, we conclude that the equation has no solution.
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