Structures of Expressions Unit Test:

Question

Use the Associated 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 that Expression 1 is equivalent to Expression 2 using the Associative Property, we will simplify both expressions and show that they yield the same result.

Expression 1:

\[ 22r - 13 \]

Expression 2:

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

Let's simplify Expression 2 step by step.

1. Simplify the parentheses in Expression 2: \[ 19r + (3r - 2) - 11 = 19r + 3r - 2 - 11 \]

2. Combine like terms:

   • Combine the \(r\) terms: \[ 19r + 3r = 22r \]
   • Combine the constant terms: \[ -2 - 11 = -13 \]

Putting these together: \[ 19r + (3r - 2) - 11 = 22r - 13 \]

Conclusion:

Both Expression 1 and Expression 2 simplify to \(22r - 13\):

• Expression 1: \(22r - 13\)
• Expression 2: \(22r - 13\)

Thus, we have shown that Expression 1 is equivalent to Expression 2 using the Associative Property, as they both yield the same result.