Question
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
Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2.
Expression 1: 22r−13
Expression 2: 19r+(3r−2)−11
Answers
GPT-4o mini
To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we will simplify both expressions and compare the results.
**Expression 1:**
\[
22r - 13
\]
**Expression 2:**
\[
19r + (3r - 2) - 11
\]
Let's simplify Expression 2 step by step:
1. Start with the expression:
\[
19r + (3r - 2) - 11
\]
2. Apply the Associative Property to rewrite the expression without parentheses:
\[
19r + 3r - 2 - 11
\]
3. Combine like terms (the \(r\) terms):
\[
(19r + 3r) - 2 - 11 = 22r - 2 - 11
\]
4. Now, combine the constant terms:
\[
22r - (2 + 11) = 22r - 13
\]
Now we have simplified Expression 2 to:
\[
22r - 13
\]
Since Expression 1 is also:
\[
22r - 13
\]
We can see that both expressions are equivalent. Thus, we have shown that:
**Expression 1** is equivalent to **Expression 2** using the Associative Property.
**Expression 1:**
\[
22r - 13
\]
**Expression 2:**
\[
19r + (3r - 2) - 11
\]
Let's simplify Expression 2 step by step:
1. Start with the expression:
\[
19r + (3r - 2) - 11
\]
2. Apply the Associative Property to rewrite the expression without parentheses:
\[
19r + 3r - 2 - 11
\]
3. Combine like terms (the \(r\) terms):
\[
(19r + 3r) - 2 - 11 = 22r - 2 - 11
\]
4. Now, combine the constant terms:
\[
22r - (2 + 11) = 22r - 13
\]
Now we have simplified Expression 2 to:
\[
22r - 13
\]
Since Expression 1 is also:
\[
22r - 13
\]
We can see that both expressions are equivalent. Thus, we have shown that:
**Expression 1** is equivalent to **Expression 2** using the Associative Property.
can you make the problem solving a little shorter
GPT-4o mini
Sure! Here’s a more concise solution:
**Expressions:**
- **Expression 1:** \( 22r - 13 \)
- **Expression 2:** \( 19r + (3r - 2) - 11 \)
**Step to simplify Expression 2:**
1. Remove parentheses:
\[ 19r + 3r - 2 - 11 \]
2. Combine like terms:
\[ (19r + 3r) - (2 + 11) = 22r - 13 \]
**Conclusion:**
Both Expression 1 and the simplified Expression 2 equal \( 22r - 13 \). Thus, \( 22r - 13 \) is equivalent to \( 19r + (3r - 2) - 11 \).
**Expressions:**
- **Expression 1:** \( 22r - 13 \)
- **Expression 2:** \( 19r + (3r - 2) - 11 \)
**Step to simplify Expression 2:**
1. Remove parentheses:
\[ 19r + 3r - 2 - 11 \]
2. Combine like terms:
\[ (19r + 3r) - (2 + 11) = 22r - 13 \]
**Conclusion:**
Both Expression 1 and the simplified Expression 2 equal \( 22r - 13 \). Thus, \( 22r - 13 \) is equivalent to \( 19r + (3r - 2) - 11 \).