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 determine which expressions are equivalent to the algebraic expression \( 5(3x+9) \), we can simplify the original expression first:

1. Distribute the \( 5 \): \[ 5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45 \]

Now, let's evaluate the responses provided:

1. 8x + 14 - Not equivalent.
2. 5×3x + 5×9 - This simplifies to \( 15x + 45 \), which is equivalent.
3. 5×3x + 9 - This simplifies to \( 15x + 9 \), not equivalent.
4. 15x + 9 - Not equivalent.
5. 15x + 45 - This is equivalent.

The equivalent expressions are:

• 5×3x + 5×9
• 15x + 45