According to the Associative Property, which expression is equivalent to 30m+(21m-53)+(18-2m)?

To apply the Associative Property, we can regroup the expression \( 30m + (21m - 53) + (18 - 2m) \) without changing its value.

Let's break down the expression step by step:

1. The original expression is: \[ 30m + (21m - 53) + (18 - 2m) \]

2. We can group the terms differently. The Associative Property allows us to change the grouping of the numbers: \[ (30m + 21m) + (18 - 53 - 2m) \]

3. Calculate the first part: \[ (30m + 21m) = 51m \]

4. Combine the constants and the remaining variable terms:

   • From \( (18 - 53) \): \[ 18 - 53 = -35 \] And we subtract \( 2m \) from it later.

5. Therefore, we can write the expression as: \[ 51m + (-35 - 2m) \] which simplifies to: \[ 51m - 35 - 2m \]

So you can regroup the expression into: \[ (30m + 21m) + (18 - 53 - 2m) \] Or, represented differently, we can write: \[ 51m + (-53 + 18) - 2m \]

Now, let’s compare this with the answer choices:

A. \( 51m + (-53 + 18) - 2m \): This choice matches our expression and is thus equivalent.

B. \( (30m + 21m) + (18 - 2m) \): This is another way to write the initial expression.

C. \( (49 - 53) - 16 \): This does not match.

D. \( 53m - 35 \): This also doesn't match as we have a different coefficient on \( m \).

Therefore, the answer that matches according to the Associative Property is:

A. \( 51m + (-53 + 18) - 2m \).