Question
$$7(4x+4) = -7(-4x-4)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 7(4x+4) &= -7(-4x-4)&& \text{simplify left and right hand side} \\[1 em]28x+28 &= -(-28x-28)&& \\[1 em]28x+28 &= 28x+28&& \text{move the $ \color{blue}{ 28x } $ to the left side and $ \color{blue}{ 28 }$ to the right} \\[1 em]28x-28x &= 28-28&& \text{simplify left and right hand side} \\[1 em]28x-28x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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