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 \( 5(3x + 9) \):
- 8x + 14: This is not equivalent.
- 5×3x + 5×9: This is equivalent, as it represents the distributive property applied.
- 5×3x + 9: This is not equivalent.
- 15x + 9: This is not equivalent.
- 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