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

Question

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 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 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.

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 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.
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Answer 1

The mistake made by the student is in Step 2.

In Step 1, after distributing, the correct expression is \(2x - 4 + 5x = 24\), which can be simplified. The student incorrectly combines the terms in Step 2.

The correct simplification should be: \[2x + 5x - 4 = 24\] which results in: \[7x - 4 = 24.\]

Instead of finding \(10x - 4 = 24\), it should have been \(7x - 4 = 24\).

Therefore, the correct response is: Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.