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

Answer 1

To show that Expression 1 ( \(22r - 13\) ) is equivalent to Expression 2 ( \(19r + (3r - 2) - 11\) ) using the Associative Property, we'll simplify Expression 2 step by step.

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

### Step 1: Simplify the expression inside the parentheses
The expression inside the parentheses is \(3r - 2\).

### Step 2: Apply the Associative Property
We can rearrange and group the terms. Let's first rewrite the expression:
\[
19r + 3r - 2 - 11
\]

According to the Associative Property, we can group the \(19r\) and \(3r\) together.

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

### Step 4: Combine the constants
Now simplify \(-2 - 11\):
\[
22r - 13
\]

### Conclusion
We find that by simplifying Expression 2, we arrive at:
\[
22r - 13
\]

This is exactly the same as Expression 1. Therefore, we have demonstrated that:
\[
22r - 13 \equiv 19r + (3r - 2) - 11
\]

Thus, Expression 1 is equivalent to Expression 2 using the Associative Property.