To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, let's begin with both expressions:
Expression 1:
\[ 22r - 13 \]
Expression 2:
\[ 19r + (3r - 2) - 11 \]
Now, we'll simplify Expression 2 step by step:
Step 1: Distribute and simplify the parentheses in Expression 2.
\[ 19r + (3r - 2) - 11 \]
\[ = 19r + 3r - 2 - 11 \]
Step 2: Combine like terms. The terms \(19r\) and \(3r\) can be combined:
\[ = (19r + 3r) + (-2 - 11) \]
\[ = 22r - 13 \]
Now we have:
Final Expression:
\[ 22r - 13 \]
Since both Expression 1 and the simplified Expression 2 yield the same result, we can conclude:
Expression 1 (22r - 13) is equivalent to Expression 2 (19r + (3r - 2) - 11).
This demonstrates the equivalence using the Associative Property, which allows us to regroup and combine terms without changing the result.