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A student solves the following problem: 2(x - 2) + 5x = 24

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?

(1 point)
Responses

Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.

Step 3: The student should have subtracted 4 from both sides, not added 4.
Step 3: The student should have subtracted 4 from both sides, not added 4.

Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 1: The student should have only distributed the 2 and x, not the x & -2.

Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
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1 answer

The mistake in the student's solution occurs in Step 2.

  1. In Step 1, the student correctly simplified the equation to \(2x - 4 + 5x = 24\).
  2. In Step 2, the student incorrectly combined \(2x\) and \(5x\). The correct sum should be \(2x + 5x = 7x\), not \(10x\).

So the correct response is:

Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.