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

Answer 1

The mistake occurs in Step 2. The student incorrectly combined the terms after distributing. The correct combination of terms in Step 2 should be:

Step 1: \( 2(x - 2) + 5x = 24 \) leads to \( 2x - 4 + 5x = 24 \).

In Step 2, the student incorrectly wrote this as \( 10x - 4 = 24 \), when it should actually be \( 7x - 4 = 24 \).

Thus, the mistake is in Step 2: the student should have added \( 2x + 5x = 7x \), not multiplied \( 2x \) and \( 5 \) to get \( 10x \).

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