Question

select all expressions that are equivalent to this algebraic expression

5 (3x + 9)

8x + 14

5 x 3x + 5 x 9

5 x 3x + 9

15x + 9

15x + 45

Answer 1

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

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

Now we have simplified \( 5(3x + 9) \) to \( 15x + 45 \).

Next, we will compare this result with each expression provided:

1. **\( 8x + 14 \)** - Not equivalent, since it is neither in the form of \( 15x + 45 \).

2. **\( 5 \cdot 3x + 5 \cdot 9 \)** - This is equivalent since it simplifies to \( 15x + 45 \).

3. **\( 5 \cdot 3x + 9 \)** - Not equivalent, since it simplifies to \( 15x + 9 \), which is not the same.

4. **\( 15x + 9 \)** - Not equivalent, it does not match \( 15x + 45 \).

5. **\( 15x + 45 \)** - Equivalent, this matches exactly with our simplified expression.

Based on this analysis, the equivalent expressions to \( 5(3x + 9) \) are:

- \( 5 \cdot 3x + 5 \cdot 9 \)
- \( 15x + 45 \)