Question

Use the associative property to demonstrate that expression one is equivalent expression
25r - 15
20R + (5r - 3) - 12

Answer 1

To demonstrate that the two expressions \( 25r - 15 \) and \( 20r + (5r - 3) - 12 \) are equivalent using the associative property, we first simplify the second expression step by step.

### Expression 1:
\[
25r - 15
\]

### Expression 2:
\[
20r + (5r - 3) - 12
\]

### Step 1: Apply the Associative Property
The associative property states that the way in which numbers are grouped in addition or multiplication does not affect their sum or product. We will group the terms in Expression 2.

### Step 2: Simplify Expression 2
Starting from:
\[
20r + (5r - 3) - 12
\]

We can rewrite it as:
\[
20r + 5r - 3 - 12
\]
Here, we have grouped \(20r\) and \(5r\) together and combined the constants \(-3\) and \(-12\).

### Step 3: Combine like terms
Now we combine the \(r\) terms and the constant terms:
\[
(20r + 5r) + (-3 - 12) = 25r - 15
\]

### Conclusion
We find that:
\[
20r + (5r - 3) - 12 = 25r - 15
\]

Thus, both expressions are equivalent:
\[
25r - 15 = 20r + (5r - 3) - 12
\]

Therefore, using the associative property, we have shown that \( 25r - 15 \) is equivalent to \( 20r + (5r - 3) - 12 \).