Question

Under the commutative property of addition, which of the following is not equivalent to the expression 4x + 5x + 6x + 9

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

Answer 1

To determine which of the given expressions is not equivalent to \(4x + 5x + 6x + 9\), we will simplify each expression and compare them.

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

2. **First Expression**:
\[
4x + 6x + 5x + 9 = (4x + 6x + 5x) + 9 = 15x + 9
\]
This expression simplifies to \(15x + 9\).

3. **Second Expression**:
\[
6x + 9 + 5x + 4x = (6x + 5x + 4x) + 9 = 15x + 9
\]
This expression simplifies to \(15x + 9\).

4. **Third Expression**:
\[
4 + 5x + 6x + 9x = 4 + (5x + 6x + 9x) = 4 + 20x
\]
This expression simplifies to \(20x + 4\).

5. **Fourth Expression**:
\[
9 + 4x + 5x + 6x = 9 + (4x + 5x + 6x) = 9 + 15x = 15x + 9
\]
This expression simplifies to \(15x + 9\).

Now, we can compare the simplified forms from above:

- **First Expression**: \(15x + 9\)
- **Second Expression**: \(15x + 9\)
- **Third Expression**: \(20x + 4\)
- **Fourth Expression**: \(15x + 9\)

The expression **not equivalent** to \(4x + 5x + 6x + 9\) is the **third expression** \(4 + 5x + 6x + 9x\), which simplifies to \(20x + 4\).