A student solved an equation, as shown

1/4 (8 - 12x) = x -2(2x+1)
2 - 3x = x - 4x + 2
2 - 3x = -3x + 2
2 - 3x + 3x = -3x + 3x + 2
2=2
Based on the student's work, complete the statement below.
The student solved the equation ____
because the original equation has___
.