C.) infinitely many solutions.
Given the equation, x - 2(x -6) = -x + 12:
x - 2(x -6) = -x + 12
Distribute -2 into the terms inside the parenthesis:
x - 2(x -6) = -x + 12
x - 2x + 12 = -x + 12
Combine like terms:
-x + 12 = - x + 12
Subtract 12 from both sides:
-x + 12 - 12 = - x + 12 - 12
- x = - x
Add x to both sides:
- x + x = - x + x
0 = 0 (true statement).
This means that any value of x will satisfy the equation, thereby making it infinitely many solutions.
