To demonstrate the equivalence of the two expressions using the associative property, we first need to simplify expression 2 step by step.
Expression 1: \[ 22r - 13 \]
Expression 2: \[ 19r + (3r - 2) - 11 \]
Now, let's simplify expression 2:
- Distribute and combine like terms in expression 2: \[ 19r + (3r - 2) - 11 = 19r + 3r - 2 - 11 \]
- Combine \(19r\) and \(3r\): \[ 19r + 3r = 22r \] So, expression 2 rewrites to: \[ 22r - 2 - 11 \]
- Combine constants \(-2\) and \(-11\): \[ -2 - 11 = -13 \] Thus, expression 2 simplifies to: \[ 22r - 13 \]
Now we can see that:
Expression 1: \[ 22r - 13 \]
Expression 2: (after simplification) \[ 22r - 13 \]
Since both expressions are equal, we have demonstrated their equivalence using the associative property through the process of simplification. Thus, we conclude: \[ 22r - 13 = 22r - 13 \]
Both expressions are equivalent.