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:
- Combine the \( m \) terms: \( 30m + 21m - 2m = 49m \)
- Combine the constant terms: \( -53 + 18 = -35 \)
Putting it all together, we have: \[ 49m - 35 \]
Now let's evaluate the options given:
- 53m - 35: Not equivalent
- (30m + 21m) + (18 - 2m): This shows the associative property, but not simplified fully. It’s equivalent structurally but does not simplify to the final value.
- 51m + (-53 + 18) - 2m: This would also need more simplification, but overall, it should resolve to something different.
- (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: \[ \text{(30m + 21m) + (18 - 2m)} \]