Question

Use the associative property to demonstrate that expression one is equivalent expression too expression 125r - 15 expression 2 20R +( 5r - 3 )- 12

Answer 1

To demonstrate that the two expressions are equivalent using the associative property, let's first write down both expressions clearly:

1. Expression 1: \( 125r - 15 \)
2. Expression 2: \( 20r + (5r - 3) - 12 \)

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

Step 1: Start with Expression 2:
\[
20r + (5r - 3) - 12
\]

Step 2: Apply the associative property. We can rearrange the terms inside the parentheses:
\[
20r + 5r - 3 - 12
\]

Step 3: Combine like terms:
- Combine \( 20r \) and \( 5r \):
\[
(20r + 5r) - 3 - 12 = 25r - 3 - 12
\]

Step 4: Now combine -3 and -12:
\[
25r - 15
\]

So, we have simplified Expression 2 to:
\[
25r - 15
\]

Now we can compare both expressions:

- Expression 1: \( 125r - 15 \)
- Expression 2: \( 25r - 15 \)

Since the two expressions aren't equal as they have different coefficients for \( r \), \( 125r - 15 \neq 25r - 15 \).

It seems there is an error in your interpretation, as the expressions given are not equivalent. If you meant to have different expressions or if there is a misunderstanding, please clarify the original expressions.