I thought number 4 on this list was incorrect but didn't know how to fully explain it here is the list that I have.
Please look at the following simplification of an algebraic expression. Which line contains the mistake and why?
Line 1: (2x + 6x) + 4y + 3x - 2xy
Line 2: (8x) + 4y + 3x - 2xy
Line 3: 8x + 3x + 4y - 2xy
Line 4: 11x + 4y - 2xy
Line 5: 13xy
Line 4 is ok: 8x+3x = 11x
Line 5 is bogus. You cannot combine x,y,xy terms.
Line 4 is as far as you can go.
To determine if there is a mistake in the simplification of the algebraic expression, we can simplify each line and compare them to the original expression.
Given the original expression: (2x + 6x) + 4y + 3x - 2xy
Let's simplify each line:
Line 1: (2x + 6x) + 4y + 3x - 2xy
Combining like terms:
8x + 4y + 3x - 2xy
Line 2: (8x) + 4y + 3x - 2xy
No further simplification needed.
Line 3: 8x + 3x + 4y - 2xy
Combining like terms:
11x + 4y - 2xy
Line 4: 11x + 4y - 2xy
No further simplification needed.
Line 5: 13xy
Comparing the simplified expressions to the original expression, we can see that Line 1, Line 3, Line 4, and Line 5 are all correct. However, Line 2 is incorrect because it does not include the term 6x. The term 6x was mistakenly omitted, resulting in an incorrect simplification.
Therefore, the mistake is in Line 2 because it is missing the term 6x.