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?
A. Step 3: The student should have subtracted 4 from both sides, not added 4.
B. Step 1: The student should have only distributed the 2 and x, not the x & -2.
C. Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
D. Step 5: The student should have multiplied by 10 on both sides, not divided by 10.

Answer 1

are you sure this is correct

Answer 2

The mistake in the student's solution occurs in **Step 2**. The student incorrectly combined the terms \(2x\) and \(5x\) to arrive at \(10x\) rather than the correct \(7x\). So, the correct answer is:

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

Answer 3

Let's go through the student's steps carefully:

The original equation is:

\[ 2(x - 2) + 5x = 24 \]

**Step 1:**
The student distributes \(2\):
\[ 2x - 4 + 5x = 24 \]

This step is correct.

**Step 2:**
The student combines like terms:
\[ 2x + 5x - 4 = 24 \]
which should yield:
\[ 7x - 4 = 24 \]

The student's equation mistakenly states:
\[ 10x - 4 = 24 \]

This is the point where the mistake occurs. Therefore, the error is correctly identified in:

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

So, the previous conclusion was indeed correct: the mistake lies in Step 2.