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)
The equation solved correctly would show that it has infinitely many solutions.
is that right gbt
Yes, that is correct. The equation given has infinitely many solutions.
infinitely is not an answer
Apologies for the confusion. The correct answer is "no solution." The equation simplifies to 4 = 4, which is a contradiction. Therefore, there is no value of x that satisfies the equation, resulting in no solution.
The student's work correctly shows that the equation has infinitely many solutions.
The student made a mistake in their solution for the given equation. Let's go through the steps and identify where the error occurred.
The original equation is:
2(2x+2) = 4(x+4)
Expanding the left side of the equation, we get:
4x + 4 = 4(x+4)
Now, let's simplify the equation step by step:
Step 1: Distribute the 4 on the right side:
4x + 4 = 4x + 16
Step 2: Combine like terms on each side:
4x - 4x = 16 - 4
This simplifies to:
0 = 12
We have reached an inconsistency where 0 does not equal 12. There are no values of x that would satisfy this equation. This means that the equation has no solutions, not infinitely many solutions as the student incorrectly concluded.
So, to correctly solve this equation, we would say that it has no solution.