To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we first write down the two expressions:
Expression 1: \( 22r - 13 \)
Expression 2: \( 19r + (3r - 2) - 11 \)
Now, let's simplify Expression 2 step by step.
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Distribute and combine like terms in Expression 2: \[ 19r + (3r - 2) - 11 \] The expression inside the parentheses is already simplified, so we can rewrite it as: \[ 19r + 3r - 2 - 11 \]
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Combine like terms:
- Combine \( 19r \) and \( 3r \): \[ 19r + 3r = 22r \]
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Now combine the constant terms:
- Combine \(-2\) and \(-11\): \[ -2 - 11 = -13 \]
Putting this together, we get: \[ 22r - 13 \]
Now, we can check the final form of Expression 2: \[ 22r - 13 \]
Since both expressions are \( 22r - 13 \), we have shown that:
\[ 22r - 13 = 19r + (3r - 2) - 11 \]
Thus, using the Associative Property, we've demonstrated that Expression 1 is equivalent to Expression 2: \[ \text{Expression 1} = \text{Expression 2} \]