Question

Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2. 22r - 13 19r + (3r - 2) - 11

Answer 1

To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we first write down the two expressions:

**Expression 1:** \( 22r - 13 \)

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

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

1. **Distribute and combine like terms in Expression 2**:
\[
19r + (3r - 2) - 11
\]
The expression inside the parentheses is already simplified, so we can rewrite it as:
\[
19r + 3r - 2 - 11
\]

2. **Combine like terms**:
- Combine \( 19r \) and \( 3r \):
\[
19r + 3r = 22r
\]

3. **Now combine the constant terms**:
- Combine \(-2\) and \(-11\):
\[
-2 - 11 = -13
\]

Putting this together, we get:
\[
22r - 13
\]

Now, we can check the final form of Expression 2:
\[
22r - 13
\]

Since both expressions are \( 22r - 13 \), we have shown that:

\[
22r - 13 = 19r + (3r - 2) - 11
\]

Thus, using the Associative Property, we've demonstrated that Expression 1 is equivalent to Expression 2:
\[
\text{Expression 1} = \text{Expression 2}
\]