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


(2 points)

Answer 1

To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, let's begin with both expressions:

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

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

Now, we'll simplify Expression 2 step by step:

**Step 1:** Distribute and simplify the parentheses in Expression 2.
\[ 19r + (3r - 2) - 11 \]
\[ = 19r + 3r - 2 - 11 \]

**Step 2:** Combine like terms. The terms \(19r\) and \(3r\) can be combined:
\[ = (19r + 3r) + (-2 - 11) \]
\[ = 22r - 13 \]

Now we have:
**Final Expression:**
\[ 22r - 13 \]

Since both Expression 1 and the simplified Expression 2 yield the same result, we can conclude:

**Expression 1 (22r - 13) is equivalent to Expression 2 (19r + (3r - 2) - 11).**

This demonstrates the equivalence using the Associative Property, which allows us to regroup and combine terms without changing the result.