To determine which expression is equivalent to \( 30m + (21m - 53) + (18 - 2m) \) using the Associative Property, we first need to simplify the expression.
The original expression is:
\[
30m + (21m - 53) + (18 - 2m)
\]
We can remove the parentheses since addition is associative:
\[
30m + 21m - 53 + 18 - 2m
\]
Next, we can combine like terms:
1. Combine the \( m \) terms: \( 30m + 21m - 2m = 49m \)
2. Combine the constant terms: \( -53 + 18 = -35 \)
Putting it all together, we have:
\[
49m - 35
\]
Now let's evaluate the options given:
1. **53m - 35**: Not equivalent
2. **(30m + 21m) + (18 - 2m)**: This shows the associative property, but not simplified fully. Itβs equivalent structurally but does not simplify to the final value.
3. **51m + (-53 + 18) - 2m**: This would also need more simplification, but overall, it should resolve to something different.
4. **(49m - 53) + 16**: This is not equivalent either.
Based on all our evaluations, the best expression that shows the equivalency through the associative property is:
\[
(30m + 21m) + (18 - 2m)
\]
So the correct answer is:
\[
\text{(30m + 21m) + (18 - 2m)}
\]