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
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.
The student made multiple errors in their steps. Here's a breakdown of the errors:
Error 1 (Step 1): When distributing the -2 to both terms inside the parentheses (4 and 3x), the student neglected to multiply -2 with 4. The correct first step should be: 8x - 2(4) - 2(3x) = 8x - 8 - 6x.
Error 2 (Step 2): The student combined the like terms 8x and 3x incorrectly. They should have subtracted 6x from 8x, not added. The correct second step should be: 8x - 8 - 6x = 2x - 8.
Error 3 (Step 3): The student correctly simplified the expression 2x - 8 to 11x - 8. However, this step is incorrect because the previous step was wrong.
Error 4 (Step 4): Finally, the student claims that 11x - 8 is equivalent to 3x, which is incorrect. These two expressions are not equivalent.
In summary, the student made errors in each step of their solution. They did not correctly distribute -2, made a mistake when combining like terms, and claimed that two non-equivalent expressions are equal.
Let's go through each step and identify the errors:
Step 1: 8x - 8 + 3x
Here, the student correctly distributed the -2 to both terms inside the parentheses, which gives us -8 - 6x. However, they made a mistake in combining like terms when adding 8x and 3x together. The correct expression should be 11x - 8 - 6x.
Step 2: 8x + 3x - 8
In this step, the student combined 8x and 3x correctly, resulting in 11x. However, they neglected to include the term -6x from the previous step. The correct expression should be 11x - 6x - 8.
Step 3: 11x - 8
The student correctly combined 11x and -6x, resulting in 5x. However, they made an error when bringing down the -8. The correct expression should be 5x - 8.
Step 4: 3x
In this step, the student claims that the expression 5x - 8 is equivalent to 3x. This is incorrect. The expression 5x - 8 is not equivalent to 3x.
Overall, the student made mistakes in steps 1, 2, and 3 when combining like terms and neglecting to include certain terms. As a result, the final claim in step 4 is also incorrect.