Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2.Expression 1: 22r−13 Expression 2: 19r+(3r−2)−11 (2 points)

Answer 1

To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we will simplify both expressions and show they result in the same value.

Expression 1:

\[ 22r - 13 \]

Expression 2:

\[ 19r + (3r - 2) - 11 \]

Now, let's simplify Expression 2 step by step:

1. Begin with: \[ 19r + (3r - 2) - 11 \]

2. Apply the Associative Property. First, we can simplify the part inside the parentheses: \[ 19r + 3r - 2 - 11 \]

3. Now, combine like terms: \[ (19r + 3r) + (-2 - 11) \] This gives us: \[ 22r - 13 \]

Now we've simplified Expression 2 to: \[ 22r - 13 \]

Conclusion: Since both Expression 1 and Expression 2 simplify to \( 22r - 13 \), we have shown that:

\[ 22r - 13 = 19r + (3r - 2) - 11 \]

Thus, using the Associative Property, we demonstrate that Expression 1 is indeed equivalent to Expression 2.