Question
$$3(2x-1)-x = 5(x-2)+7$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 3(2x-1)-x &= 5(x-2)+7&& \text{simplify left and right hand side} \\[1 em]6x-3-x &= 5x-10+7&& \\[1 em]5x-3 &= 5x-3&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]5x-5x &= -3+3&& \text{simplify left and right hand side} \\[1 em]5x-5x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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