To solve the equation \(-2(-x + 9) = 2(x - 9)\), let's first simplify both sides step by step.
Starting with the left side:
\[ -2(-x + 9) = -2(-x) + -2(9) = 2x - 18 \]
Now simplifying the right side:
\[ 2(x - 9) = 2x - 18 \]
Now substituting the simplified sides back into the equation, we have:
\[ 2x - 18 = 2x - 18 \]
This shows that both sides of the equation are identical, which means that any value of \(x\) will satisfy this equation. Therefore, it is classified as an identity.
This means the equation has infinitely many solutions.