Question

Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.
x + x + 6 – 7 + x
2x + 2 + x
3 – x + 2x – 4 + 2x
x – 1
x + 1

Answer 1

First simplify the given expression:
6 + (−x) + 2x + (−7) + 2x = (−x + 2x + 2x) + (6 − 7) = 3x − 1.

Now simplify each choice:
- x + x + 6 − 7 + x = 3x − 1 → equivalent
- 2x + 2 + x = 3x + 2 → not equivalent
- 3 − x + 2x − 4 + 2x = 3x − 1 → equivalent
- x − 1 = x − 1 → not equivalent
- x + 1 = x + 1 → not equivalent

So the equivalent expressions are: x + x + 6 − 7 + x and 3 − x + 2x − 4 + 2x.