2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Infinitely many solutions
Based on the student's work, the equation was solved (Blank)
The equation solved correctly would show that it has (Blank)
solution(s).
3 answers
Based on the student's work, the equation was solved correctly.
The equation solved correctly would show that it has infinitely many solution(s).
This is because the final equality \(4 = 4\) is always true, indicating that the original equation is an identity and holds for all values of \(x\).
Given the choices you've provided, the answer for the second part would be no solutions.
The correct interpretation of the final equation \(4 = 4\) indicates that the original equation is true for all \(x\), which actually suggests that it has infinitely many solutions. However, since "infinitely many solutions" is not among the answer choices given (one, two, three, or no solutions), the phrasing or context might imply that the options relate to the fact that the equation ultimately simplifies to a tautology.
In traditional algebraic settings, if the outcome leads to a true statement that isn't contingent on \(x\), the understanding typically leans toward "no unique solutions" in a problem-solving context, leading to the conclusion:
