5. A student solved the following equation using the following steps:2(2x+2)=4(x+4)4x+4=4x+44=4Infinitely 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).Skip to navigation

Answer 1

Let's analyze the steps provided by the student:

1. The student starts with the equation:
   $2(2x+2)=4(x+4)$

2. Distributing on both sides yields:

   • Left side: $2(2x)+2(2)=4x+4$
   • Right side: $4(x)+4(4)=4x+16$

   Thus, we have: $4x+4=4x+16$

3. Next, the student subtracts $4x$ from both sides: $4=16$

4. The equation $4=16$ is false. This suggests that the original equation does not possess a solution for $x$. Instead, it indicates that the two expressions are not equal for any value of $x$, implying no solutions exist.

Given these steps, we can conclude:

• The student's work correctly shows that the original equation leads to a contradiction.
• Therefore, the correct conclusion should be that the original equation has no solutions.

If you have any further questions or need clarification on any part, feel free to ask!