To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we first need to simplify Expression 2.
Expression 1:
\[ 22r - 13 \]
Expression 2:
\[ 19r + (3r - 2) - 11 \]
Let's simplify Expression 2 step by step.
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Start with Expression 2: \[ 19r + (3r - 2) - 11 \]
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Apply the Associative Property, which states that the way in which numbers are grouped in addition or subtraction does not affect their sum or difference. We can regroup the terms: \[ = 19r + 3r - 2 - 11 \]
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Now, combine like terms:
- Combine \(19r\) and \(3r\): \[ = (19r + 3r) - 2 - 11 \] \[ = 22r - 2 - 11 \]
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Combine the constant terms \(-2\) and \(-11\): \[ = 22r - (2 + 11) \] \[ = 22r - 13 \]
Now we see that Expression 2 simplifies to the same result as Expression 1:
Final result:
\[ 22r - 13 \]
Therefore, we have shown that: \[ 22r - 13 \equiv 19r + (3r - 2) - 11 \]
Thus, by using the Associative Property, we have demonstrated that Expression 1 is equivalent to Expression 2.