Question

According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m)?(1 point)
Responses

(49m−53)+16
left parenthesis 49 m minus 53 right parenthesis plus 16

(30m+21m)+(18−2m)
left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis

53m−35
53 m minus 35

51m+(−53+18)−2m

Answer 1

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.

1. Start with the original expression:
\[
30m + (21m - 53) + (18 - 2m)
\]

2. Combine the terms inside the parentheses:
\[
30m + 21m - 53 + 18 - 2m
\]

3. Now, combine the like terms:
- For the \(m\) terms: \(30m + 21m - 2m = 49m\)
- For the constant terms: \(-53 + 18 = -35\)

4. Now, we can rewrite the expression:
\[
49m - 35
\]

Now we compare it with the provided options:

1. \((49m - 53) + 16\)
2. \((30m + 21m) + (18 - 2m)\)
3. \(53m - 35\)
4. \(51m + (-53 + 18) - 2m\)

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)**.