To determine which expressions are equivalent to the algebraic expression \( 5(3x+9) \), we can simplify the original expression first:
- Distribute the \( 5 \): \[ 5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45 \]
Now, let's evaluate the responses provided:
- 8x + 14 - Not equivalent.
- 5×3x + 5×9 - This simplifies to \( 15x + 45 \), which is equivalent.
- 5×3x + 9 - This simplifies to \( 15x + 9 \), not equivalent.
- 15x + 9 - Not equivalent.
- 15x + 45 - This is equivalent.
The equivalent expressions are:
- 5×3x + 5×9
- 15x + 45