Are the expressions 3+(4x+1)

Question

and 4−4x
equivalent?(1 point)
Responses

No, they are not because 3+(4x+1)
simplifies to 4+4x
, which is not equivalent to 4−4x
.
No, they are not because 3 minus left parenthesis 4 x plus 1 right parenthesis simplifies to 2 minus 4 x , which is not equivalent to 4 minus 4 x .

Yes, they are because both expressions simplify to 4−4x
.
Yes, they are because both expressions simplify 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 x+1
, which is not equivalent to 4−4x
.
No, they are not because 3 minus left parenthesis 4 x plus 1 right parenthesis simplifies to x plus 1 , which is not equivalent to 4 minus 4 x .

Answer 1

To determine whether the expressions \( 3 + (4x + 1) \) and \( 4 - 4x \) are equivalent, we can simplify each expression:

1. Simplifying \( 3 + (4x + 1) \): \[ 3 + (4x + 1) = 3 + 4x + 1 = 4 + 4x \]

2. The second expression \( 4 - 4x \) remains unchanged.

Now, we need to compare \( 4 + 4x \) and \( 4 - 4x \):

• The first expression simplifies to \( 4 + 4x \).
• The second expression is \( 4 - 4x \).

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

Conclusion:

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