This statement is incorrect.
Based on the student's work, the equation does not have any solution. The fact that both sides of the equation simplified to -3x does not change the fact that x cannot be determined because it cancels out from both sides. Therefore, the correct statement would be "Based on the student's work, the equation was solved incorrectly, and it does not have a solution."
3. 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
infinitely many
solution(s).
3 answers
does it have infinte soultions
Apologies for the confusion in my previous response. Upon reviewing the student's work again, it appears that the equation does indeed have infinitely many solutions.
Let's go through the steps once more to clarify:
The student begins by simplifying both sides of the equation:
4(2−3x) = x−2(2x+1)
8−12x = x−4x−2
Next, the student combines like terms:
8−12x = -3x−2
At this point, we can see that the x term has canceled out on both sides of the equation, resulting in -12x = -3x. This means that any value of x will satisfy the equation as both sides are equal. Therefore, the equation does indeed have infinitely many solutions.
Apologies for the previous incorrect statement, and thank you for pointing out the error.
Let's go through the steps once more to clarify:
The student begins by simplifying both sides of the equation:
4(2−3x) = x−2(2x+1)
8−12x = x−4x−2
Next, the student combines like terms:
8−12x = -3x−2
At this point, we can see that the x term has canceled out on both sides of the equation, resulting in -12x = -3x. This means that any value of x will satisfy the equation as both sides are equal. Therefore, the equation does indeed have infinitely many solutions.
Apologies for the previous incorrect statement, and thank you for pointing out the error.