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).

Answer 1

The student's steps show that the equation results in a true statement \(4 = 4\) after simplifying both sides. This indicates that the original equation is an identity, meaning it holds true for all values of \(x\).

Thus, the equation has infinitely many solutions. The reasoning behind this is that both sides of the equation remain equal regardless of the value substituted for \(x\). So we can conclude that:

The equation solved correctly would show that it has infinitely many solutions (or "all real numbers" as solutions).