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

53m - 35

51m + (-53 + 18) - 2m

(30m + 21m) + (18 - 2m)

(49m - 53) +16

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

To find an expression equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange and group the terms without changing their sums.

Starting with the expression:

\[
30m + (21m - 53) + (18 - 2m)
\]

1. We can rearrange it by grouping the \(m\) terms and the constants:
\[
(30m + 21m - 2m) + (-53 + 18)
\]

2. Now, let's simplify the terms:
- For the \(m\) terms:
\[
30m + 21m - 2m = 30m + 21m = 51m \quad \text{and then} \quad 51m - 2m = 49m
\]
- For the constant terms:
\[
-53 + 18 = -35
\]

Thus, we have:
\[
49m - 35
\]

So, the equivalent expression is:
\[
(49m - 53) + 16
\]

In summary, the equivalent expression is:
\[
(49m - 53) + 16
\]

Therefore, the answer is:
\((49m - 53) + 16\)