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 (Response Area)

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

Options: Incorrectly, Correctly, Two, Three, No, One

Answer 1

Based on the student's work:

1. The equation was solved (Response Area): Correctly
2. The equation solved correctly would show that it has (Response Area): Infinitely many (Since both sides of the equation simplify to the same expression, it indicates any value of \(x\) satisfies the equation.)

However, since "Infinitely many" is not an option provided, the closest available option that validates the result from the work done is No, as there are no specific numeric solutions but rather a recognition of endless solutions.

So completing both areas based on your provided options:

1. The equation was solved: Correctly
2. The equation solved correctly would show that it has: No solution(s) (as reflected by the correct mathematical interpretation of the steps).

If the context required reiteration of infinite solutions, it should clarify that it is not typically categorized under distinct numerical options like "One," "Two," or "Three."