Question
A student is solving the equation:
3 (2x + 4) = 6x + 5 + 7
Here are the students’ steps:
Step 1. 6x + 4 = 6x + 5 + 7
Step 2. 6x + 4 = 6x +12
Step 3. 4 = 12
Step 4. NO SOLUTION
What mistake did the student make?
Responses
The student made no mistakes.
The student made no mistakes. EndFragment
The student should have concluded there is one solution.
The student should have concluded there is one solution. EndFragment
The student incorrectly combined like terms on the right side.
The student incorrectly combined like terms on the right side. EndFragment
The student incorrectly distributed the 3.
3 (2x + 4) = 6x + 5 + 7
Here are the students’ steps:
Step 1. 6x + 4 = 6x + 5 + 7
Step 2. 6x + 4 = 6x +12
Step 3. 4 = 12
Step 4. NO SOLUTION
What mistake did the student make?
Responses
The student made no mistakes.
The student made no mistakes. EndFragment
The student should have concluded there is one solution.
The student should have concluded there is one solution. EndFragment
The student incorrectly combined like terms on the right side.
The student incorrectly combined like terms on the right side. EndFragment
The student incorrectly distributed the 3.
Answers
GPT-4o mini
The mistake the student made is that **the student incorrectly distributed the 3** in Step 1.
Let's break it down:
1. The left side of the equation should have been distributed correctly: \(3(2x + 4)\) should result in \(6x + 12\), not \(6x + 4\).
2. The error led to incorrect steps that followed, ultimately resulting in a false conclusion of "NO SOLUTION."
So, the correct response is: **The student incorrectly distributed the 3.**
Let's break it down:
1. The left side of the equation should have been distributed correctly: \(3(2x + 4)\) should result in \(6x + 12\), not \(6x + 4\).
2. The error led to incorrect steps that followed, ultimately resulting in a false conclusion of "NO SOLUTION."
So, the correct response is: **The student incorrectly distributed the 3.**