Question

Are the expressions 3+(4x+1)
and 4−4x
equivalent?(1 point)
Responses

Yes, they are because both expressions simplify to 4−4x
.
Yes, they are because both expressions simplify to 4 minus 4 x .

No, they are not because 3+(4x+1)
simplifies to x+1
, which is not equivalent to 4−4x
.
No, they are not because 3 plus left parenthesis 4 x plus 1 right parenthesis simplifies to x plus 1 , which is not equivalent to 4 minus 4 x .

Yes, they are because both expressions simplify to 0.
Yes, they are because both expressions simplify to 0.

No, they are not because 3+(4x+1)
simplifies to 4+4x
, which is not equivalent to 4−4x
.

Answer 1

To determine whether the expressions \(3 + (4x + 1)\) and \(4 - 4x\) are equivalent, let's simplify the first expression:

1. Start with \(3 + (4x + 1)\).
2. Distributing and combining like terms, we get:
\[
3 + 4x + 1 = 4 + 4x
\]

Now we have \(4 + 4x\) and need to compare this to \(4 - 4x\).

Clearly, \(4 + 4x\) is not equivalent to \(4 - 4x\).

Therefore, the correct response is:

**No, they are not because \(3 + (4x + 1)\) simplifies to \(4 + 4x\), which is not equivalent to \(4 - 4x\).**