Apply the Commutative Property to generate an expression equivalent to 8+9f−2+6f−8f−4+12 .(1 point)

To apply the Commutative Property, we can rearrange the terms in the expression without changing their values.

Starting with the expression: 8 + 9f - 2 + 6f - 8f - 4 + 12

We can rearrange the terms in any order. Let's group the terms with 'f' together and constants (numbers without 'f') together:

= (8 - 2 - 4) + (9f + 6f - 8f) + 12

Simplifying each group separately:

= 2 + 7f + 12

Combining the constants:

= 14 + 7f

So, the expression equivalent to 8 + 9f - 2 + 6f - 8f - 4 + 12 using the Commutative Property is:

B. 14 + 7f

WRONG

I apologize for the mistake. Let's try again.

Starting with the expression: 8 + 9f - 2 + 6f - 8f - 4 + 12

We can rearrange the terms using the Commutative Property:

= (8 - 2 - 4) + (9f + 6f - 8f) + 12

Simplifying each group separately:

= 2 + 7f + 12

Combining the constants:

= 14 + 7f

So, the expression equivalent to 8 + 9f - 2 + 6f - 8f - 4 + 12 using the Commutative Property is:

B. 14 + 7f

Lucinda uses properties of operations to write an expression equivalent to 9+3(5−a)−7a. Which could be the expression that Lucinda wrote?(1 point)

Let's simplify the given expression step by step.

Start with the given expression: 9 + 3(5 - a) - 7a

First, distribute the 3 to the terms inside the parentheses:
= 9 + 15 - 3a - 7a

Combining like terms:
= 24 - 10a

Therefore, the expression equivalent to 9 + 3(5 - a) - 7a is 24 - 10a.

So, the correct answer is:
Lucinda could have written D. 24 - 10a.

Which expression is equivalent to 12c − d?(1 point)

The expression 12c - d cannot be simplified any further since there are no like terms to combine or any other mathematical operations to perform. Therefore, the expression 12c - d is already in its simplest form and is equivalent to itself.

So, the correct answer is D. 12c - d.

Which expression is equivalent to 12c−d?(1 point)

3(4c+d)−2d

4(3c−d)−5d

4d+3c−5d

4(d+3c)−5d

To find the expression equivalent to 12c - d, we can distribute the coefficients to the terms inside the parentheses and simplify.

Starting with the expression: 12c - d

We can distribute the coefficients:

= 3(4c + d) - 2d

Expanding the parentheses:

= 12c + 3d - 2d

Combining like terms:

= 12c + d

Therefore, the expression equivalent to 12c - d is:

A. 3(4c + d) - 2d