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 demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we first need to simplify Expression 2.

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

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

Let's simplify Expression 2 step by step.

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

2. Apply the Associative Property, which states that the way in which numbers are grouped in addition or subtraction does not affect their sum or difference. We can regroup the terms:
\[ = 19r + 3r - 2 - 11 \]

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

4. Combine the constant terms \(-2\) and \(-11\):
\[ = 22r - (2 + 11) \]
\[ = 22r - 13 \]

Now we see that Expression 2 simplifies to the same result as Expression 1:

**Final result:**
\[ 22r - 13 \]

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

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