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