Question
$$5(x+6)-2x = 3(x+10)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 5(x+6)-2x &= 3(x+10)&& \text{simplify left and right hand side} \\[1 em]5x+30-2x &= 3x+30&& \\[1 em]3x+30 &= 3x+30&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 30 }$ to the right} \\[1 em]3x-3x &= 30-30&& \text{simplify left and right hand side} \\[1 em]3x-3x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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