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
51 m plus left parenthesis negative 53 plus 18 right parenthesis minus 2 m

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To find the expression equivalent to \( 30m + (21m - 53) + (18 - 2m) \) using the Associative Property, let's first simplify the expression step by step.

1. Start by removing the parentheses:
\[
30m + 21m - 53 + 18 - 2m
\]

2. Combine like terms:
- Combine the \(m\) terms: \(30m + 21m - 2m = 49m\)
- Combine the constant terms: \(-53 + 18 = -35\)

So, the combined expression becomes:
\[
49m - 35
\]

Now, among the given options, we are looking for an expression equivalent to \(49m - 35\).

The correct equivalent expression is:
\[
53m - 35
\]
is incorrect because it exceeds the m term count.

The correct answer based on our simplification process is:
\[
(49m - 53) + 16
\]

In summary, the expression you have that is equivalent to \( 30m + (21m - 53) + (18 - 2m) \) is:
- \( (49m - 53) + 16 \)