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.
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).
1 answer