To find which step in Max's solution could lead to a conclusion that the equation has no solution, we need to analyze each option to see if it leads to an inconsistency when solved.
A. 3(x+4) = x + 4 \[ 3x + 12 = x + 4 \ 3x - x + 12 = 4 \ 2x + 12 = 4 \ 2x = 4 - 12 \ 2x = -8 \ x = -4 \] This has a solution.
B. 3(x+4) = x + 12 \[ 3x + 12 = x + 12 \ 3x - x + 12 = 12 \ 2x + 12 = 12 \ 2x = 12 - 12 \ 2x = 0 \ x = 0 \] This has a solution.
C. 3(x+4) = 3x + 12 \[ 3x + 12 = 3x + 12 \] This equation is an identity (true for all x), which means it has infinitely many solutions, not no solution.
D. 3(x+4) = 3x + 4 \[ 3x + 12 = 3x + 4 \ 3x - 3x + 12 = 4 \ 12 = 4 \] This is a contradiction (false statement), which indicates that there is no solution.
The correct answer is D. This step leads Max to conclude that the equation has no solution.
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