To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we need to manipulate Expression 2 to see if we can get it to look like Expression 1.
Expression 1: \[ 22r - 13 \]
Expression 2: \[ 19r + (3r - 2) - 11 \]
Step 1: Simplify Expression 2
Start by simplifying Expression 2:
-
Distribute and simplify the terms in the parentheses. \[ 19r + 3r - 2 - 11 \]
-
Now combine like terms:
- Combine \(19r\) and \(3r\): \[ (19r + 3r) - 2 - 11 = 22r - 2 - 11 \]
-
Next, combine \(-2\) and \(-11\): \[ 22r - (2 + 11) = 22r - 13 \]
Conclusion
After simplifying Expression 2, we find that: \[ 22r - 13 \]
This matches Expression 1: \[ 22r - 13 \]
Thus, by using the Associative Property and simplifying, we have shown that Expression 1 is equivalent to Expression 2.
Therefore, we conclude that: \[ 22r - 13 \equiv 19r + (3r - 2) - 11 \]
1 answer