A student solved the following equation using the following steps:
2(2x + 2) = 4(x + 4)
4x + 4 = 4x + 4
4 = 4
Infinite solutions
Based on the student's work, the equation was solved ____ .
The equation solved correctly would show that it has _____ solution(s)
The student's work is incorrect and does not solve the equation.
The equation has infinitely many solutions because both sides simplify to the same expression:
2(2x + 2) = 4(x + 4)
4x + 4 = 4x + 16
4x + 4x = 16 - 4
8x = 12
x = 3/2
Therefore, the equation has one solution.
The equation was solved incorrectly.
The equation solved incorrectly would show that it has infinite solutions.
The student's work shows that they simplified both sides of the equation correctly, resulting in the equation 4 = 4. However, in this case, we can see that both sides of the equation are equal, meaning that the equation is true no matter what value x takes. In other words, any value of x would satisfy the equation. Therefore, we conclude that the equation has infinite solutions.
So, based on the student's work, the equation was solved correctly. The equation solved correctly would show that it has infinite solutions.