Question
a student claims that 8x - 2 (4 + 3x) is equivalent to 3x describe all the errors in there steps
step 1: 8x - 8 + 3x
step 2: 8x + 3x - 8
step 3: 11x - 8
step 4: 3x
step 1: 8x - 8 + 3x
step 2: 8x + 3x - 8
step 3: 11x - 8
step 4: 3x
Answers
GPT-4
There are many errors in the student's steps.
1. The first error is in step 1. The student incorrectly distributed -2 to (4 + 3x).
The correct distribution should be -2*4 = -8 and -2*3x = -6x, not -8 and 3x.
2. Due to that mistake, the equation from step 1 should be 8x - 8 - 6x.
3. In step 2, again, due to the mistake in step 1, the expression should have been reordered to 8x - 6x - 8, not 8x + 3x - 8.
4. In step 3, when combining like terms, instead of it being 11x - 8, it should have been 2x - 8 due to the mistake in step 1 and 2.
5. Finally, the biggest error is in step 4. After correcting the previous steps, the final expression should be 2x - 8, not 3x. So the student's claim that 8x - 2 (4 + 3x) is equivalent to 3x is incorrect.
These errors could be due to misunderstanding the concept of distribution and combining like terms.
1. The first error is in step 1. The student incorrectly distributed -2 to (4 + 3x).
The correct distribution should be -2*4 = -8 and -2*3x = -6x, not -8 and 3x.
2. Due to that mistake, the equation from step 1 should be 8x - 8 - 6x.
3. In step 2, again, due to the mistake in step 1, the expression should have been reordered to 8x - 6x - 8, not 8x + 3x - 8.
4. In step 3, when combining like terms, instead of it being 11x - 8, it should have been 2x - 8 due to the mistake in step 1 and 2.
5. Finally, the biggest error is in step 4. After correcting the previous steps, the final expression should be 2x - 8, not 3x. So the student's claim that 8x - 2 (4 + 3x) is equivalent to 3x is incorrect.
These errors could be due to misunderstanding the concept of distribution and combining like terms.