Question
$$2(4x-5)+7x = 5(3x-2)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 2(4x-5)+7x &= 5(3x-2)&& \text{simplify left and right hand side} \\[1 em]8x-10+7x &= 15x-10&& \\[1 em]15x-10 &= 15x-10&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ -10 }$ to the right} \\[1 em]15x-15x &= -10+10&& \text{simplify left and right hand side} \\[1 em]15x-15x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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