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, the equation was solved incorrectly.
The equation solved correctly would show that it has infinitely many solutions.
The last answer was wrong
I apologize for the mistake. Based on the student's work, the equation was solved correctly, but it actually shows that it has no solution.
The equation 2(2x+2) = 4(x+4) simplifies to 4x+4=4x+8, but when we subtract 4x from both sides, we get 4 = 8. This is not a true statement, so there are no values of x that satisfy the equation. Therefore, the correct conclusion is that the equation has no solution.
Based on the student's work, the equation was solved incorrectly.
The equation should have been solved as follows:
2(2x + 2) = 4(x + 4)
4x + 4 = 4x + 16 (applying the distributive property)
4x - 4x = 16 - 4 (subtracting 4x from both sides)
0 = 12 (simplifying)
Since we end up with 0 = 12, which is not true, the equation has no solutions.