Question

Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2.

Expression 1: 22r−13
22
𝑟
−
13

Expression 2: 19r+(3r−2)−11

Answer 1

To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we need to manipulate Expression 2 to see if we can get it to look like Expression 1.

**Expression 1:**
\[
22r - 13
\]

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

### Step 1: Simplify Expression 2

Start by simplifying Expression 2:
1. Distribute and simplify the terms in the parentheses.
\[
19r + 3r - 2 - 11
\]

2. Now combine like terms:
- Combine \(19r\) and \(3r\):
\[
(19r + 3r) - 2 - 11 = 22r - 2 - 11
\]

3. Next, combine \(-2\) and \(-11\):
\[
22r - (2 + 11) = 22r - 13
\]

### Conclusion

After simplifying Expression 2, we find that:
\[
22r - 13
\]

This matches Expression 1:
\[
22r - 13
\]

Thus, by using the Associative Property and simplifying, we have shown that Expression 1 is equivalent to Expression 2.

Therefore, we conclude that:
\[
22r - 13 \equiv 19r + (3r - 2) - 11
\]