Question
$$13(x+17)+4x = 17(x+13)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 13(x+17)+4x &= 17(x+13)&& \text{simplify left and right hand side} \\[1 em]13x+221+4x &= 17x+221&& \\[1 em]17x+221 &= 17x+221&& \text{move the $ \color{blue}{ 17x } $ to the left side and $ \color{blue}{ 221 }$ to the right} \\[1 em]17x-17x &= 221-221&& \text{simplify left and right hand side} \\[1 em]17x-17x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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