According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m)?(1 point)

To simplify the expression \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange and regroup the terms in any way we wish.

Let's break it down step-by-step:

1. Start with the original expression:
\[
30m + (21m - 53) + (18 - 2m)
\]

2. Distribute the terms inside the parentheses:
\[
= 30m + 21m - 53 + 18 - 2m
\]

3. Now, rearranging and combining like terms:
- Combine all \(m\) terms:
\[
(30m + 21m - 2m) = 49m
\]
- Combine the constant terms:
\[
(-53 + 18) = -35
\]

4. Therefore, we obtain:
\[
49m - 35
\]

Now, let's compare this with the provided responses:

1. \( (49m - 53) + 16 \) → This is not equivalent.
2. \( 51m + (-53 + 18) - 2m \) → This simplifies to \( 51m - 35 - 2m = 49m - 35 \), which is equivalent.
3. \( (30m + 21m) + (18 - 2m) \) → This is equivalent as it maintains the grouping.
4. \( 53m - 35 \) → This is not equivalent.

Thus, the correct equivalent expression according to the Associative Property is:
\[
(30m + 21m) + (18 - 2m)
\]
This confirms that the associativity allows us to regroup terms, leading to the same final expression of \(49m - 35\).