Question

Structures of Expressions Unit Test:
Use the Associated Property to demonstrate that Expression 1 is equivalent to Expression 2.
Expression 1: 22r-13
Expression 2: 19r + (3r- 2) -11

Answer 1

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

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

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

Let's simplify Expression 2 step by step.

1. **Simplify the parentheses** in Expression 2:
\[
19r + (3r - 2) - 11 = 19r + 3r - 2 - 11
\]

2. **Combine like terms**:
- Combine the \(r\) terms:
\[
19r + 3r = 22r
\]
- Combine the constant terms:
\[
-2 - 11 = -13
\]

Putting these together:
\[
19r + (3r - 2) - 11 = 22r - 13
\]

### Conclusion:
Both Expression 1 and Expression 2 simplify to \(22r - 13\):
- Expression 1: \(22r - 13\)
- Expression 2: \(22r - 13\)

Thus, we have shown that Expression 1 is equivalent to Expression 2 using the Associative Property, as they both yield the same result.