Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10 = 28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
A. Step 3: The student should have subtracted 4 from both sides, not added 4.
B. Step 1: The student should have only distributed the 2 and x, not the x & -2.
C. Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
D. Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
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The mistake in the student's solution occurs in Step 2. The student incorrectly combined the terms \(2x\) and \(5x\) to arrive at \(10x\) rather than the correct \(7x\). So, the correct answer is:
C. Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
Let's go through the student's steps carefully:
The original equation is:
\[ 2(x - 2) + 5x = 24 \]
Step 1: The student distributes \(2\): \[ 2x - 4 + 5x = 24 \]
This step is correct.
Step 2: The student combines like terms: \[ 2x + 5x - 4 = 24 \] which should yield: \[ 7x - 4 = 24 \]
The student's equation mistakenly states: \[ 10x - 4 = 24 \]
This is the point where the mistake occurs. Therefore, the error is correctly identified in:
C. Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
So, the previous conclusion was indeed correct: the mistake lies in Step 2.
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