According to the Associative Property, which expression is equivalent to 30m + (21m - 53) + (18 - 2m)' ? (1 point) 53m - 35; (30m + 21m) + (18 - 2m); 51m + (- 53 + 18) - 2m; (49m - 53) + 16

1 answer

To determine which expression is equivalent to \( 30m + (21m - 53) + (18 - 2m) \) using the Associative Property, we first need to simplify the expression.

The original expression is: \[ 30m + (21m - 53) + (18 - 2m) \]

We can remove the parentheses since addition is associative: \[ 30m + 21m - 53 + 18 - 2m \]

Next, we can combine like terms:

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

Putting it all together, we have: \[ 49m - 35 \]

Now let's evaluate the options given:

  1. 53m - 35: Not equivalent
  2. (30m + 21m) + (18 - 2m): This shows the associative property, but not simplified fully. It’s equivalent structurally but does not simplify to the final value.
  3. 51m + (-53 + 18) - 2m: This would also need more simplification, but overall, it should resolve to something different.
  4. (49m - 53) + 16: This is not equivalent either.

Based on all our evaluations, the best expression that shows the equivalency through the associative property is: \[ (30m + 21m) + (18 - 2m) \]

So the correct answer is: \[ \text{(30m + 21m) + (18 - 2m)} \]