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 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 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.

Answer 1

The mistake occurs in Step 2. The student incorrectly combined the terms \(2x + 5x\). Instead of realizing that \(2x + 5x = 7x\), the student incorrectly concluded that this equals \(10x\).

The correct process after Step 1 should have been:

1. Start with \(2x - 4 + 5x = 24\)
2. Combine like terms correctly: \(2x + 5x = 7x\)

Thus, the correct equation after Step 1 should be:
\(7x - 4 = 24\).

Therefore, the most accurate response is:

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