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 step by step.

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

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

First, let's simplify Expression 2:

1. **Start with the expression:**
\[ 19r + (3r - 2) - 11 \]

2. **Distributing:**
Here, we can rewrite it without parentheses:
\[ 19r + 3r - 2 - 11 \]

3. **Combine like terms (using the Associative Property):**
- Combine \( 19r \) and \( 3r \):
\[ (19r + 3r) + (-2 - 11) \]
\[ 22r - 13 \]

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

Since Expression 1 is also:
\[ 22r - 13 \]

Thus, we can conclude that:
\[ 22r - 13 = 19r + (3r - 2) - 11 \]

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