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

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

4x+6x+5x+9

Answer 1

To determine which expression is not equivalent to the original expression \(4x + 5x + 6x + 9\), we can simplify the expressions provided in the options using the commutative property of addition (which states that the order of addition does not affect the sum) and by combining like terms where applicable.

1. **Original Expression**:
\[
4x + 5x + 6x + 9 = (4 + 5 + 6)x + 9 = 15x + 9
\]

2. **Option 1**: \(6x + 9 + 5x + 4x\)
\[
= (6x + 5x + 4x) + 9 = 15x + 9 \quad \text{(Equivalent)}
\]

3. **Option 2**: \(4 + 5x + 6x + 9x\)
\[
= 4 + (5x + 6x + 9x) = 4 + 20x \quad \text{(Not Equivalent)}
\]

4. **Option 3**: \(9 + 4x + 5x + 6x\)
\[
= 9 + (4x + 5x + 6x) = 9 + 15x = 15x + 9 \quad \text{(Equivalent)}
\]

5. **Option 4**: \(4x + 6x + 5x + 9\)
\[
= (4x + 6x + 5x) + 9 = 15x + 9 \quad \text{(Equivalent)}
\]

From this analysis, the expression that is **not equivalent** to the original expression \(4x + 5x + 6x + 9\) is:

**Option 2**: \(4 + 5x + 6x + 9x\).