To determine which expression is equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange the terms and group them differently.
First, let's simplify the original expression step by step:
1. Start with the original expression:
\[
30m + (21m - 53) + (18 - 2m)
\]
2. Remove the parentheses:
\[
30m + 21m - 53 + 18 - 2m
\]
3. Combine like terms:
- Combine the \(m\) terms: \(30m + 21m - 2m = 49m\)
- Combine the constant terms: \(-53 + 18 = -35\)
Thus, we have:
\[
49m - 35
\]
Now, we can examine the response options to find the one that matches \(49m - 35\).
The option that corresponds to this result is:
**53m - 35** (as that does not match).
**(49m - 53) + 16** would imply further adjustment is needed since \(49m - 53\) does not match.
**(30m + 21m) + (18 - 2m)** matches as it shows the grouping of \(30m\) and \(21m\) plus the last term.
**51m + (-53 + 18) - 2m** leads to a discrepancy in \(m\) terms.
Therefore, the correct equivalent expression using the Associative Property is:
\[
(30m + 21m) + (18 - 2m)
\]
Thus, the correct answer is:
**(30 m + 21 m) + (18 - 2 m)**.