Question

Under the Commutative Property of addition, which of the following is not equivalent to the expression 4x+5x+6x+9
(1 point)
Responses

6x+9+5x+4x
6 x plus 9 plus 5 x plus 4 x

4+5x+6x+9x
4 plus 5 x plus 6 x plus 9 x

4x+6x+5x+9
4 x plus 6 x plus 5 x plus 9

9+4x+5x+6x

Answer 1

To determine which expression is not equivalent to \(4x + 5x + 6x + 9\) under the Commutative Property of addition, let's first simplify the original expression:

\[
4x + 5x + 6x + 9 = (4 + 5 + 6)x + 9 = 15x + 9
\]

Now let's compare each of the provided options to see if they simplify to \(15x + 9\):

1. **\(6x + 9 + 5x + 4x\)**: This can be rearranged to \(6x + 5x + 4x + 9 = (6 + 5 + 4)x + 9 = 15x + 9\) (Equivalent)

2. **\(4 + 5x + 6x + 9x\)**: This is \(4 + (5 + 6 + 9)x = 4 + 20x\) (Not equivalent)

3. **\(4x + 6x + 5x + 9\)**: This can be rearranged to \(4x + 6x + 5x + 9 = (4 + 6 + 5)x + 9 = 15x + 9\) (Equivalent)

4. **\(9 + 4x + 5x + 6x\)**: This can be rearranged to \(9 + 4x + 5x + 6x = 9 + (4 + 5 + 6)x = 9 + 15x\) (Equivalent)

The only expression that is **not equivalent** to \(4x + 5x + 6x + 9\) is:

**\(4 + 5x + 6x + 9x\)**.