Question

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.