A student solved the following equation using the following steps:
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
Answer: No Solution
(2 points)
Based on the student’s work, the equation was solved correct or not?
The equation solved correctly would show that it has how many solutions?
The student's work is incorrect.
From the first step, when simplifying the left side of the equation, it should be 8 - 12x instead of 8 - 3x.
So the corrected equation would be 8 - 12x = x - 4x - 2.
Simplifying this further, we get 8 - 12x = -3x - 2.
From here, we can see that the equation is inconsistent and has no solution.
Therefore, the student's work is incorrect and the equation has no solution.