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?
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.
its step 2 ai a liar
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.
The mistake the student made is in Step 2. The student incorrectly multiplied 2(x - 2) as (2x)(5) instead of correctly distributing the 2 to both terms inside the parentheses. The correct step should be: 2(x - 2) expands to 2x - 4.
The mistake is in Step 2: the student should have added 2x + 5x to get 7x, not multiplied 2x and 5 to get 10x.
To correct this step, the student should have written:
2(x - 2) + 5x = 24
2x - 4 + 5x = 24
Then, they can combine like terms:
7x - 4 = 24
Continuing with the rest of the steps, the correct solution would be obtained.
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