Question

Use the Associative Property to demonstrate that Expression 1 is equivalent to Expression 2 Expression 1: 6x + 11 Expression 2: 8x + (-2x + 6) + 5 (7 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Simplify Expression 2 using the associative property

Answer 1

To demonstrate that Expression 1, \(6x + 11\), is equivalent to Expression 2, \(8x + (-2x + 6) + 5\), we will simplify Expression 2 using the Associative Property.

Expression 2:

\[ 8x + (-2x + 6) + 5 \]

1. Group the terms using the Associative Property: \[ 8x + (-2x + 6) + 5 = 8x + 6 + (-2x + 5) \] (Note: Reorganizing does not change the result because of the Associative Property)

2. Combine the constant terms: \[ -2x + 6 + 5 = -2x + 11 \]

3. Now substitute back into the expression: \[ 8x + (-2x + 11) \]

4. Combine like terms: \[ (8x - 2x) + 11 = 6x + 11 \]

Thus, we simplified Expression 2 to \(6x + 11\), showing that:

Expression 1: \(6x + 11\)

Expression 2 simplifies to \(6x + 11\).

Therefore, we have demonstrated that Expression 1 is equivalent to Expression 2.