Question
$$7x-8+3(x+2) = 2(5x-1)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 7x-8+3(x+2) &= 2(5x-1)&& \text{simplify left and right hand side} \\[1 em]7x-8+3x+6 &= 10x-2&& \\[1 em]10x-2 &= 10x-2&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]10x-10x &= -2+2&& \text{simplify left and right hand side} \\[1 em]10x-10x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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