5. A student solved the following equation using the following steps:

Question

2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Infinitely many solutions

(2 points)
Based on the student's work, the equation was solved

The equation solved correctly would show that it has
solution(s).

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Answer 1

The student's work shows that the equation \( 2(2x+2) = 4(x+4) \) simplifies to \( 4 = 4 \), which is a true statement. This indicates that the original equation is an identity—true for all values of \( x \).

Thus, the equation solved correctly would show that it has infinitely many solutions.

Therefore, the student is correct in stating that the equation has infinitely many solutions.