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 determine which expressions are equivalent to the algebraic expression \( 5(3x+9) \), let's first simplify \( 5(3x + 9) \):

1. Distribute the \( 5 \) across the terms inside the parentheses: \[ 5(3x + 9) = 5 \times 3x + 5 \times 9 = 15x + 45 \]

Now we can compare this result, \( 15x + 45 \), with the provided options:

1. \( 8x + 14 \) - Not equivalent.
2. \( 5 \times 3x + 5 \times 9 \) - Equivalent (this is the same as \( 15x + 45 \)).
3. \( 5 \times 3x + 9 \) - Not equivalent.
4. \( 15x + 9 \) - Not equivalent.
5. \( 15x + 45 \) - Equivalent (this matches our simplified expression).

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

• \( 5 \times 3x + 5 \times 9 \)
• \( 15x + 45 \)

So, the correct answers are:

• \( 5 \times 3x + 5 \times 9 \)
• \( 15x + 45 \)

Answer 2

a b c or d

Answer 3

Based on the equivalence to the expression \( 5(3x+9) \), the correct choices are:

B. \( 5 \times 3x + 5 \times 9 \)
D. \( 15x + 45 \)

So you would select B and D.