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 51m+(−53+18)−2m 51 m plus left parenthesis negative 53 plus 18 right parenthesis minus 2 m (30m+21m)+(18−2m) left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis 53m−35

Answer 1

To determine which expression is equivalent to \(30m + (21m - 53) + (18 - 2m)\) using the Associative Property, we can rearrange the terms and group them differently.

First, let's simplify the original expression step by step:

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

2. Remove the parentheses: \[ 30m + 21m - 53 + 18 - 2m \]

3. Combine like terms:

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

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

Now, we can examine the response options to find the one that matches \(49m - 35\).

The option that corresponds to this result is: 53m - 35 (as that does not match). (49m - 53) + 16 would imply further adjustment is needed since \(49m - 53\) does not match. (30m + 21m) + (18 - 2m) matches as it shows the grouping of \(30m\) and \(21m\) plus the last term. 51m + (-53 + 18) - 2m leads to a discrepancy in \(m\) terms.

Therefore, the correct equivalent expression using the Associative Property is: \[ (30m + 21m) + (18 - 2m) \]

Thus, the correct answer is: (30 m + 21 m) + (18 - 2 m).