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
No solution.
(2 points)
Based on the student's work, the equation was solved
incorrectly
The equation solved correctly would show that it has
solution(s).
The student's work is incorrect. If we analyze the steps, we can see where the error occurred.
First, the student distributed the 4 on the left side of the equation correctly:
4(2−3x) = 8 - 12x
Then, the student distributed the -2 on the right side of the equation correctly:
x − 2(2x+1) = x - 4x - 2 = -3x - 2
So far, the student's work is correct, but here is where the error happens:
The student equated the left side and the right side of the equation incorrectly:
8 - 12x = -3x - 2
To solve the equation, we collect like terms:
-12x + 3x = -2 - 8
Simplifying further:
-9x = -10
Finally, we divide both sides of the equation by -9:
x = -10/-9
x = 10/9
Therefore, the equation does have a solution, contrary to what the student concluded.