A student claims that 8x - 2(4+3x) is equivalent to 3x. The student steps are shown below.
Expression: 8x - 2(4+3x)
Step 1: 8x - 8 + 3x
Step 2: 8x + 3x - 8
Step 3:11x - 8
Step 4: 3x
Describe ALL errors in the student's work. (There is more than one error.) Answer like a 12 year old girl
Like, the student made like two mistakes, duh! First mistake is in Step 1. The student forgot to distribute the -2 to both the 4 and the 3x. So it should be like -2(4) - 2(3x), not -2(4+3x). Silly mistake, right? Oh, and the second mistake is in Step 2. The student like combined the 8x and 3x, but totally forgot to combine the -8 too. So it should be like 8x + 3x - 8, not 8x + 3x - 8x. Oopsie!
The student made two errors in their work. First, in Step 1, they distributed the negative sign to both the 4 and the 3x, which resulted in -8 - 6x instead of -8 + 3x. Second, in Step 2, they combined the 8x and 3x together instead of subtracting them, so they got 11x instead of 5x.
Oh my goodness, there are actually a couple of errors in the student's work! Let me explain them to you.
Error 1: In Step 1, the student didn't distribute the -2 to both the 4 and the 3x. We need to multiply -2 by both of those terms. So it should be -2 * 4 = -8, and -2 * 3x = -6x. Then, when we combine like terms, it should be 8x - 8 - 6x, not 8x - 8 + 3x.
Error 2: In Step 2, the student mixed up the signs. They wrote 8x + 3x - 8, but it should actually be 8x - 6x - 8. The 3x term should be negative because the student made an error in Step 1.
So, when we correct these errors, the correct expression is 8x - 6x - 8, which simplifies to 2x - 8. It's not equal to 3x like the student claimed.