To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we can rewrite both expressions and see if they simplify to the same result.
Expression 1:
\[ 22r - 13 \]
Expression 2:
\[ 19r + (3r - 2) - 11 \]
First, let's simplify Expression 2 step by step.
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Start with: \[ 19r + (3r - 2) - 11 \]
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Apply the Associative Property:
- The Associative Property states that the way numbers are grouped in addition does not change their sum. Therefore, we can add 3r to 19r first: \[ (19r + 3r) - 2 - 11 \]
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Simplifying \( 19r + 3r \): \[ 22r - 2 - 11 \]
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Now, combine the constant terms \(-2\) and \(-11\): \[ 22r - 13 \]
Now we can see that both expressions are equivalent:
- Expression 1: \( 22r - 13 \)
- Expression 2 simplified is also \( 22r - 13 \)
Thus, by using the Associative Property and simplifying Expression 2, we have shown that Expression 1 is equivalent to Expression 2:
\[ \boxed{22r - 13} \]