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, we can group the terms in different ways and simplify.

We'll break down the original expression step-by-step:

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

2. Group the first two terms \(30m\) and \(21m\):
\[
(30m + 21m) + (18 - 2m) - 53
\]

3. Calculate \(30m + 21m\):
\[
51m + (18 - 2m - 53)
\]

4. Simplify \(18 - 53\):
\[
51m - 35 - 2m
\]

5. Combine like terms:
\[
(51m - 2m) - 35 = 49m - 35
\]

From the options you provided:

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

The only relevant equivalent expression we simplified is:
\[
49m - 35
\]
This does not exactly match any of the above answers without further modification.

However, the most similar form that allows for step-by-step addition:
\[
(30m + 21m) + (18 - 2m)
\]

In conclusion:
The correct option that we derived through computation is not directly listed. However, based on the simplification process used to locate the correct form using elementary algebra and the associative property, we approximate to one of the expressions provided, resulting in:
\(\text{(30m + 21m) + (18 - 2m)}\)
as we reorganized our original equation with properties encouraging interpretation.