A student solves the following problem: 2(x - 2) + 5x = 24Step 1: 2x - 4 + 5x = 24Step 2: 10x - 4 = 24 Step 3: 10x - 4 + 4 = 24 + 4Step 4: 10x = 28Step 5: 10x/10=28/10Step 6: x = 2.8 Where is the mistake? What did the student do incorrectly?(1 point)ResponsesStep 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 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 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.

Answer 1

The mistake occurs in Step 3. The student incorrectly added 4 to both sides instead of subtracting it. The correct action would be to add 4 to both sides to isolate the term with \( x \).

So the correct statement for Step 3 should be:

Step 3: \( 10x - 4 + 4 = 24 + 4 \) is correct if they were to add, but they needed to adjust the earlier step first to ensure the equation balances properly.

However, the original mistake in reasoning is that after Step 2, they incorrectly claimed \( 10x - 4 = 24 \) when it should have been simplified correctly as \( 7x - 4 = 24 \).

Thus, the proper correction timeframe would be in Step 2, where \( 2x + 5x \) should have equaled \( 7x \) instead of \( 10x \). Hence, the response indicating Step 2 is the next logical error to point to, and effectively misleading since it’s part of the process before isolating.

In conclusion, the accurate errors and their nature are likely alluded to in Steps 2 and 3 within the overall solution travel.