Question
$$12x+1 = 3(4x+1)-2$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 12x+1 &= 3(4x+1)-2&& \text{simplify right side} \\[1 em]12x+1 &= 12x+3-2&& \\[1 em]12x+1 &= 12x+1&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]12x-12x &= 1-1&& \text{simplify left and right hand side} \\[1 em]12x-12x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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