Question
$$x\cdot6-2x\cdot5+x\cdot4+x\cdot3-x-8 = x\cdot6-2x\cdot5+x\cdot4+x\cdot3-x-8$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} x\cdot6-2x\cdot5+x\cdot4+x\cdot3-x-8 &= x\cdot6-2x\cdot5+x\cdot4+x\cdot3-x-8&& \text{simplify left and right hand side} \\[1 em]6x-10x+4x+3x-x-8 &= 6x-10x+4x+3x-x-8&& \\[1 em]2x-8 &= 2x-8&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]2x-2x &= -8+8&& \text{simplify left and right hand side} \\[1 em]2x-2x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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