Question
$$\frac{1}{3}(3x-12) = x-4$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} \frac{1}{3}(3x-12) &= x-4&& \text{simplify left side} \\[1 em]\frac{3x-12}{3} &= x-4&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{3x-12}{3} &= 3x-3\cdot4&& \text{cancel out the denominators} \\[1 em]3x-12 &= 3x-12&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]3x-3x &= -12+12&& \text{simplify left and right hand side} \\[1 em]3x-3x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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