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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

1 answer

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!