Select all expressions that are equivalent to this algebraic expression:

Question

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