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?

1 answer

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.