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 the equivalence of the two expressions using the associative property, we first need to simplify expression 2 step by step.

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

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

Now, let's simplify expression 2:

1. **Distribute and combine like terms in expression 2:**
\[
19r + (3r - 2) - 11 = 19r + 3r - 2 - 11
\]
2. **Combine \(19r\) and \(3r\):**
\[
19r + 3r = 22r
\]
So, expression 2 rewrites to:
\[
22r - 2 - 11
\]
3. **Combine constants \(-2\) and \(-11\):**
\[
-2 - 11 = -13
\]
Thus, expression 2 simplifies to:
\[
22r - 13
\]

Now we can see that:

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

**Expression 2:** (after simplification)
\[
22r - 13
\]

Since both expressions are equal, we have demonstrated their equivalence using the associative property through the process of simplification. Thus, we conclude:
\[
22r - 13 = 22r - 13
\]

Both expressions are equivalent.