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

Answer 1

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.

Answer 2

can you make the problem solving a little shorter

Answer 3

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 \( 19r + (3r - 2) - 11 \).