Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2. Expression 1:%C2%A0 22r−13 Expression 2:%C2%A0 19r+(3r−2)−11

Answer 1

To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we can rewrite both expressions and see if they simplify to the same result.

Expression 1:

\[ 22r - 13 \]

Expression 2:

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

First, let's simplify Expression 2 step by step.

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

2. Apply the Associative Property:

   • The Associative Property states that the way numbers are grouped in addition does not change their sum. Therefore, we can add 3r to 19r first: \[ (19r + 3r) - 2 - 11 \]

3. Simplifying \( 19r + 3r \): \[ 22r - 2 - 11 \]

4. Now, combine the constant terms \(-2\) and \(-11\): \[ 22r - 13 \]

Now we can see that both expressions are equivalent:

• Expression 1: \( 22r - 13 \)
• Expression 2 simplified is also \( 22r - 13 \)

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

\[ \boxed{22r - 13} \]