Question
$$x-2(5x+5) = 5-9x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x-2(5x+5) &= 5-9x&& \text{simplify left and right hand side} \\[1 em]x-(10x+10) &= -9x+5&& \\[1 em]x-10x-10 &= -9x+5&& \\[1 em]-9x-10 &= -9x+5&& \text{move the $ \color{blue}{ -9x } $ to the left side and $ \color{blue}{ -10 }$ to the right} \\[1 em]-9x+9x &= 5+10&& \text{simplify left and right hand side} \\[1 em]-9x+9x &= 15&& \\[1 em]0 &= 15&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 15 } $ is FALSE, we conclude that the equation has no solution.
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