To determine which expression is equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, let's simplify the given expression step by step.
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Start with the original expression: \[ 30m + (21m - 53) + (18 - 2m) \]
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Combine the terms inside the parentheses: \[ 30m + 21m - 53 + 18 - 2m \]
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Now, combine the like terms:
- For the \(m\) terms: \(30m + 21m - 2m = 49m\)
- For the constant terms: \(-53 + 18 = -35\)
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Now, we can rewrite the expression: \[ 49m - 35 \]
Now we compare it with the provided options:
- \((49m - 53) + 16\)
- \((30m + 21m) + (18 - 2m)\)
- \(53m - 35\)
- \(51m + (-53 + 18) - 2m\)
The expression we simplified to is \(49m - 35\).
None of the options produce exactly \(49m - 35\) directly, but the interpretation involves rearranging the expressions.
The closest we have based on associative grouping is the second option: \[ (30m + 21m) + (18 - 2m) \text{ since it correctly complies with associativity, but needs further simplification.} \]
However, our final simplified form of \(49m - 35\) is inconsistent with any direct choice as none is perfectly equal to this.
So the answer aligning closest with the associative property would remain:
Response: (30m + 21m) + (18 - 2m).