To find the expression that is equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange and group the terms.
We start with the expression: \[ 30m + (21m - 53) + (18 - 2m) \]
Using the Associative Property of addition, we can rearrange the terms: \[ (30m + 21m + (18 - 2m)) - 53 \]
Now, let's break it down:
- Combine the \(m\) terms: \[ 30m + 21m - 2m = 49m \]
- Then add the constants: \[ 18 - 53 = -35 \] So we get: \[ 49m - 35 \]
Defining the options:
- A: \((49m - 53) + 16\)
- B: \(53m - 35\)
- C: \(51m + (-53 + 18) - 2m\)
- D: \((30m + 21m + (18 - 2m))\)
Now comparing our derived expression \(49m - 35\) with the options:
- Option A evaluates to \(49m - 53 + 16 = 49m - 37\) (not equivalent)
- Option B gives \(53m - 35\) (not equivalent)
- Option C simplifies to \(51m - 35 - 2m = 49m - 35\) (equivalent)
- Option D is just a regrouping of the original expression and does not provide a single simplified equivalent expression.
Thus, the answer is: C: \(51m + (-53 + 18) - 2m\), since it simplifies to \(49m - 35\).
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