To apply the Associative Property, we can regroup the terms in the expression \( 30m + (21m - 53) + (18 - 2m) \) without changing their order.
Let's start by simplifying the original expression:
\[
30m + (21m - 53) + (18 - 2m)
\]
First, we can combine like terms. Rearranging and grouping accordingly gives us:
\[
(30m + 21m - 2m) + (-53 + 18)
\]
Now, we can combine:
1. For the \(m\) terms:
\[
30m + 21m - 2m = 49m
\]
2. For the constants:
\[
-53 + 18 = -35
\]
Putting it all together, we get:
\[
49m - 35
\]
Let's compare this with the provided options:
1. **51m + (−53 + 18) - 2m**
- Not equivalent.
2. **(30m + 21m) + (18 - 2m)**
- This is equivalent based on the Associative Property, as it simply rearranges the terms.
3. **53m - 35**
- Not equivalent.
4. **(49m - 53) + 16**
- Not equivalent.
Thus, the expression **(30m + 21m) + (18 - 2m)** is equivalent to the original expression using the Associative Property.