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

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).

Based on the student's work, it appears that the equation has infinitely many solutions. This is because when the student simplified the equation, they ended up with "4=4." This means that both sides of the equation are equal, and therefore, any value of x will satisfy the equation.

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
.

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

Based on the student's work, it appears that the equation has no solution. This is because when the student simplified the equation, they ended up with "8−3x=−3x−2." In this form, it is clear that the variable "x" cancels out on both sides of the equation, resulting in the inequality "8=-2," which is not true. Therefore, there is no value of x that satisfies the equation.

The student's work shows that the equation is solved correctly, but it does not show that the equation has any solution(s). The final step of the student's work simplifies to "4=4", which means that both sides of the equation are equal. This implies that the equation is an identity and holds true for any value of x. Therefore, the equation has infinitely many solutions.