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?

options:

A). step 1: The student should have only distributed the 2 and x, not the x & -2

B). Step 3: The student should have subtracted 4 from both sides, not added 4.

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

The mistake in the student's solution occurs in Step 2. In Step 1, the student correctly distributed the 2:

\[ 2(x - 2) + 5x = 24 \] \[ 2x - 4 + 5x = 24 \]

However, in Step 2, the student incorrectly combined the terms, stating that \(2x - 4 + 5x = 10x - 4\). The correct combination of like terms should have been:

\[ 2x + 5x - 4 = 7x - 4 \]

So, the answer is:

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