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?

Responses

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 5: The student should have multiplied by 10 on both sides, not divided by 10.

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

Answer 1

The mistake is in Step 3. The student incorrectly added 4 to both sides of the equation instead of subtracting 4. The correct step should be:

Step 3: 10x - 4 - 4 = 24 - 4

Answer 2

its step 2 ai a liar

Answer 3

I apologize if my previous response was incorrect. Let's go through the steps again to determine the mistake.

Step 1: Distribute 2 to (x - 2) and we get 2x - 4 + 5x = 24.

Step 2: Combine like terms on the left side of the equation: 2x + 5x = 7x. The equation now becomes 7x - 4 = 24.

Step 3: Add 4 to both sides of the equation to isolate the variable term: 7x - 4 + 4 = 24 + 4. This simplifies to 7x = 28.

Step 4: Divide both sides of the equation by 7 to solve for x: 7x/7 = 28/7. This simplifies to x = 4.

After reviewing the steps again, it seems that all the steps are correct and there is no mistake. Therefore, the student did not do anything incorrectly.