Question

Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use? Check all that apply.
3 x minus 3 + 4 = 2 minus x minus 3
3 x minus 1 + 4 = 2 minus x + 3
3 x minus 3 + 4 = 2 minus x + 3
3 x + 1 = negative x minus 1
3 x + 3 = negative x + 5
3 x + 1 = negative x + 5

Answer 1

Start from 3(x − 1) + 4 = 2 − (x + 3).

Distribute both sides: 3x − 3 + 4 = 2 − x − 3, which simplifies to 3x + 1 = −x − 1.

So the equivalent equations are:
- 3x − 3 + 4 = 2 − x − 3 (matches the distributed form)
- 3x + 1 = −x − 1 (the simplified form)

The others have sign/distribution mistakes (they give +3 or +5 on the right or fail to multiply −1 by 3).