Question

Select all expressions that are equivalent to this algebraic expression:

5(3x+9)


(1 point)
Responses

8x+14
8 x plus 14

5×3x+5×9
5 times 3 x plus 5 times 9

5×3x+9
5 times 3 x plus 9

15x+9
15 x plus 9

15x+45

Answer 1

To simplify the expression \( 5(3x + 9) \), we can use the distributive property:

\[
5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45
\]

Now, let's examine the provided responses to identify which ones are equivalent to \( 5(3x + 9) \):

1. **8x + 14**: This is not equivalent.
2. **5×3x + 5×9**: This is equivalent, as it represents the distributive property applied.
3. **5×3x + 9**: This is not equivalent.
4. **15x + 9**: This is not equivalent.
5. **15x + 45**: This is equivalent, as it matches the simplified expression.

The expressions that are equivalent to \( 5(3x + 9) \) are:

- **5×3x + 5×9**
- **15x + 45**