is 22r-13 equivalent to19r+(3r-2)-11

Question

associative property

Answer 1

To determine if \( 22r - 13 \) is equivalent to \( 19r + (3r - 2) - 11 \) using the associative property, we first simplify the right side of the equation.

Let's simplify \( 19r + (3r - 2) - 11 \):

1. Start with the expression:
   \[ 19r + (3r - 2) - 11 \]

2. Now, simplify inside the parentheses:
   \[ 19r + 3r - 2 - 11 \]

3. Combine like terms:
   \[ (19r + 3r) + (-2 - 11) = 22r - 13 \]

Now we find that: \[ 19r + (3r - 2) - 11 = 22r - 13 \]

Therefore, \( 22r - 13 \) is equivalent to \( 19r + (3r - 2) - 11 \).

The associative property was used here in the sense that the grouping of the terms in the expression did not affect the result during simplification. Thus, both expressions are indeed equivalent.